The two main activities of inferential statistics are using sample data to
estimate a population parameter (such as estimating the population mean with a confidence interval), and
test a hypothesis or claim made about a population parameter.
Hypothesis test
conducting hypothesis tests as described in this chapterconducting hypothesis tests as described in this chapter be sure to consider:
A process that uses sample statistics to test a claim about the value of a population parameter.
the context of the data
the source of the data
the sampling method used to obtain the sample data
Rare Event Rule for Inferential Statistics
If, under a given assumption, the probability of a particular observed event is exceptionally small, we conclude that the assumption is probably not correct
The _______ is a statement that the value of some population parameter (such as a population mean) is equal to some claimed value
null hypothesis (denoted by H0)
test this null hypothesis directly by assuming that it is true;either_______H0 or _______ H0 based on our hypothesis test results
reject , fail to reject
The ________ is the statement that the population parameter has a value that differs from the claimed value in the null hypothesis
alternative hypothesis denoted by H1, Ha, or HA
The symbolic form of the alternative hypothesis must use one of these symbols: ?
>, <, or inequality symbol
If you are conducting a study and want to use a hypothesis test to support your claim, the claim must be worded so that it becomes ?
the alternative hypothesis, H1, because the null hypothesis can never be proven.
If you are using a hypothesis test to test someone else's claim, then the claim can be worded so that ?
it is either H0 or H1.
H0 and H1 is written in one of these ways
H0: ? = k
H1: ? > k
or
H0: ? = k
H1: ? < k
or
H0: ? = k
H1: ? ? k
You always assume_______and examine the sampling distribution on the basis of this assumption.
? = k
A social research company claims that no more than 30% of 12 year old children have consumed beer.
The claim can be expressed symbolically as P less than or equal to .30
if this claim is false: p>.30
A university publicizes that the proportion of its students who graduate in 4 years is 82%.
H0: p = 0.82 Equality condition (Claim)
H1: p ? 0.82 Inequality condition
A water faucet manufacturer announces that the mean flow rate of a certain model of faucet is less than 2.5 gallons per minute.
H0: ? = 2.5 gal per min- Equality condition
H1: ? < 2.5 gal per min= Inequality condition (Claim)
A cereal company advertises that the mean weight of the contents of its 20-ounce size cereal boxes is more than 20 ounces.
H0: ? = 20 ounces- Equality condition
H1: ? > 20 ounces Inequality condition (Claim)
The _______ is a value used in making a decision about the null hypothesis
test statistic
If we are testing a claim about a population proportion, the sample statistic is ?.
To conduct our hypothesis test we convert to a standardized z-score with the assumption that the null hypothesis is?
Phat
true.
If we are testing a claim about a population mean, the sample statistic is ?
Xbar
Assuming we do not know the population standard deviation, to conduct our hypothesis test we convert _____ to a standardized t-score with the assumption that the null hypothesis is true.
Xbar
No matter which hypothesis represents the claim, always begin the hypothesis test by assuming ?
that the equality condition in the null hypothesis is true.
A ______ error occurs if the null hypothesis is rejected when it is actually true.
type I or alpha
A _______ error occurs if the null hypothesis is not rejected when it is actually false.
type II or beta
The USDA limit for salmonella contamination for chicken is 20%. A government meat inspector claims that the chicken produced by a company exceeds the USDA limit. You perform a hypothesis test to determine whether the meat inspector's claim is true. When w
H0: p= .2
H1: p> .2 (claim)
A type I error is rejecting H0 when it is true. [The actual proportion of contaminated chicken is less than or equal to 0.2, but you decide to reject H0.]
A type II error is failing to reject H0 when it is false.
[The actual pr
A government meat inspector claims that the chicken produced by a company exceeds the USDA limit.When will a type I or type II error occur? Which is more serious?
With a type I error, you might create a health scare and hurt the sales of chicken producers who were actually meeting the USDA limits
With a type II error, you could be allowing chicken that exceeded the USDA contamination limit to be sold to consumers.
A government meat inspector claims that the chicken produced by a company exceeds the USDA limit.When will a type I or type II error occur? Which is more serious?
With a type II error, you could be allowing chicken that exceeded the USDA contamination limit to be sold to consumers.
A type II error could result in sickness or even death
the level of significance is
the maximum allowable probability of making a type I error.
Denoted by alpha , the lowercase Greek letter alpha.
By setting the level of significance at a small value, you are saying that you want the probability of rejecting a true null hypothesis to be ?
small
Commonly used levels of significance:
.01,.025,.05,.10
The probability of making a type II error is denoted as ?
The probability of making a type II error is denoted as P(type II error) = ? (beta)
After stating the null and alternative hypotheses and specifying the level of significance, a random sample is taken from the population and a ______ is calculated.
sample statistic
The sample statistic that is compared with the population parameter used in the null hypothesis is called the ?
test statistic
The critical region (or rejection region) is ?.
the set of all values of the test statistic that cause us to reject the null hypothesis
what is any value that separates the critical region (where we reject the null hypothesis) from the fail to reject region.
A critical value
the critical value depend on ?
The critical value(s) depend on the nature of the null hypothesis, the sampling distribution that applies, and the significance level .
The P-value (or probability value) is the probability of getting a test statistic value that is
at least as extreme as the one determined from the sample data, assuming that the null hypothesis is true
for a two tailed test, the critical region is in two tails so the pvalue is?
P-value = twice the area in the tail beyond the test statistic
The null hypothesis is rejected if?
.
the test statistic falls into the rejection region.
We fail to reject the null hypothesis if ?
the test statistic falls into the fail to reject region
The null hypothesis is rejected if the P-value of the test statistic is less than or equal to ?
the significance level, .
We fail to reject the null hypothesis if the P-value is greater than ?
alpha
P-value =
probability of getting a test statistic at least as extreme as the one representing the sample data value
p=?
population proportion
The P-value for a hypothesis test is P = 0.0237. What is your decision if the level of significance is
1. alpha = 0.05?
...
Find the P-value for a left-tailed hypothesis test with a test statistic of z = -2.23. Decide whether to reject H0 if the level of significance is = 0.01.
Normal CDF( -10000,-2.23) = .0129
this is greater than .01 so you should fail to reject H0
Find the P-value for a two-tailed hypothesis test with a test statistic of z = 2.14. Decide whether to reject H0 if the level of significance is = 0.05.
For a two-tailed test, P = 2(Area right of 2.14) use:
Normal CDF( 2.14, 10,000) = .0168
now multiply this number by two ( because it takes into account both tails)
.0168 *2 =.0324
this is less than 5% so you should reject H0
The null? hypothesis, is a statement that the value of a population parameter? (such as? proportion, mean, or standard? deviation) is equal to?.
some claimed value
The alternative? hypothesis, is the statement that the parameter has a value that _________ from the null hypothesis.
somehow differs
Identify the type I error and the type II error that correspond to the given hypothesis: the % of adults who have a job is equal to 88%
Reject the null hypothesis that the percentage of adults who have a job is equal to 88% when that percentage is actually equal to 88 %;
type I error is the mistake of rejecting the null hypothesis when?
it is actually true.
A hypothesis test? (or test of? significance) is a procedure for ______ about a property of a population.
testing a claim
The? _____________ states that? if, under a given? assumption, the probability of a particular observed event is extremely? small, we conclude that the assumption is probably not correct
The rare event rule
if, under a given? assumption, the probability of a particular observed event is extremely? small, we conclude that the assumption is probably not correct.
The rare event rule
The null hypothesis? (denoted by Upper H0?) is a statement that the value of a population parameter? (such as? proportion, mean, or standard? deviation) is_____ to some claimed value.
equal
The? P-value is the probability of getting a value of the test statistic that is at least as ______as the one representing the sample data.
extreme
The test statistic is a value used in making a decision about the null hypothesis. It is found by converting the ______ _______? to a score? with the assumption that the null hypothesis is true.
sample statistic
If the? P-value is? small, such as 0.05 or? less, the null hypothesis is ?
rejected
The? P-value does not separate the critical region from the values that do not lead to rejection of the null hypothesis. The? P-value is not a value on the horizontal? axis, it is an ?
area
The inequality symbol in the alternative hypothesis points in the direction of ?
the critical region.
The tails in a distribution are the extreme critical regions bounded by?
critical values.
The symbol not equal s? is often expressed in computer science as? <>, and this is a great reminder that an alternative hypothesis with the symbol not equals? corresponds to a ?
two tailed test.
Note that? ____is not always the significance level used for hypothesis testing decision making. A higher or lower percentage may be used based on the seriousness of an incorrect decision.
5%
The power of a hypothesis test is the probability ?(1-??) of rejecting a false null hypothesis. The value of the power is computed by ?
using a particular significance level and a particular value of the population parameter that is an alternative to the value assumed true in the null hypothesis.
Identify the type I error and the type II error that corresponds to the given hypothesis.
The proportion of settled medical malpractice suits is .26
1. reject the claim that the proportion of settled malpractice suits is 0.260.26 when the proportion is actually 0.26
2. type II? error: Fail to reject the claim that the proportion of settled malpractice suits is 0.260.26 when the proportion is actually
identifying the null and alternative hypotheses.
Identify the claim to be tested and put it in symbolic form.
2.Give the symbolic form that must be true when the original claim is false.
3. Of the two symbolic expressions obtained so? far, let the alternative hypothesis H1 be the one not containing? equ
Claim: A coin favors heads when? tossed, and there are 12 heads in 26 tosses.
There is not sufficient evidence to support the claim because there are not substantially more heads than tails
When testing claims about a population proportion, the critical value method and the P-value method are ?
equivalent and will yield the same result since both methods use the same standard deviation based on the claimed proportion p.
TI-83/84 technology
Use normalcdf for finding _____and use invNorm for?
P-values, Critical values
Critical Value Method:
If z is in the critical region, then reject ?
H0.
formulate a conclusion:
carter motor company claims that the new sedan, vibra averages at least 30 miles per gallon in the city. We decided to reject the null hypothesis. how do you word this?
There is sufficient evidence to warrant rejection of the claim that the Vibra will average at least 30 mpg in the city.
An Entomologist claims that fewer than 4 in 1000 male fireflies are unable to produce light due to a genetic mutation. We decided to reject the null hypothesis. how do you word this?
There is sufficient evidence to support the claim that the true proportion of fireflies that are unable to produce light due to a genetic mutation is less than 4 in a thousand.
the manufacturer produces refrigerator systems that are supposed to maintain a true mean temp of 49 degrees, the owner of a brewery doesn't agree and claims that he can prove the mean temperature is incorrect. the data makes us fail to reject the null hyp
There is not sufficient evidence to support the claim that the mean temperature is different from 49 degrees F.
a cereal compnay claim that the mean weight of the cereal in its packets are at least 14 ounces. the data makes us fail to reject the null hypothesis (accept it). how do we word the conclusion?
There is not sufficient evidence to reject the claim that the mean weight of the cereal packets is at least 14 oz.
A researcher claims that the amounts of acetaminophen in cold tablets have a standard deviation greater than the 3.3 standard deviation that the manufacturer reports.
We decided to reject the null hypothesis. how do you word this?
There is sufficient evidence to support the claim that the amount of acetaminophen in the cold tablets have a standard deviation greater than 3.3 mg.
an engineer claims that the mean life of a particular light bulb is 6.7 years
We decided to reject the null hypothesis. how do you word this?
. There is sufficient evidence to reject the claim that the particular model of light bulb has a mean life of 6.7 years
a researcher claims that the proportion of americans that have seen a UFO is no more than 2 in every 10000. the conclusion is to fail to reject the null (accept the claim) . How do you word this?
There is not sufficient evidence to reject the claim that the proportion of Americans that have seen a UFO is no more than 2 in ten thousand.
a psychologist claims that more than 29 % suffer from professional problems due to extreme shyness. If we fail to reject the null (accept it) how would we word the conclusion?
There is not sufficient evidence to support the claim that the true proportion of the population that suffer professional problems due to extreme shyness is more than 29%.
In a study, 57 out of 104 randomly selected pregnant women correctly guessed the sex of their babies.
Use this sample data to test the claim that the success rate of such guesses is no different from the 50% success rate expected with random chance guesse
Go to Stat, test, 1-PropZtest (5)
plug in p,x,n
select <, >, or inequality sign and calculate. the result is .3268
this is more than .05 SO:
there is not sufficient evidence to reject the claim that women who guess the sex of their babies have a success r
A research center claims that less than 22% of internet users in the US have a wireless network in their home. In a random sample of 100 adults, 12% said they have a wireless network in their home. At the significance level = 0.01, is there enough evidenc
Stat, Test 1-PropZtest
choose <p
Z= -2.41
p =.0080
this is less than .01 so we conclude: There is sufficient evidence to reject the null hypothesis in support of the claim that less than 22% of internet users in the US have a wireless network in their hom
Zogby International claims that 45% of people in the United States support making cigarettes illegal. You decide to test this claim and ask a random sample of 200 people whether they support making cigarettes illegal. Of the 200 people, 49% support such a
either its 45% or its not. So choose inequality sign.
find P by multiplying .49 by 200
plug in
x=.98
n=200
p=.45
Z= 1.14 so you should accept the Null: there is not enough evidence to reject the claim that 45% of people in the U.S. support making cigarett
Research Center claims that more than 55% of U.S. adults regularly watch their local television news. You test this claim and ask a random sample of 425 adults whether they regularly watch their local news. Of the 425 adults, 255 respond yes. At ? = 0.05
plug into Stat, Test 1-PropZtest
x=255
n=425
p=.55
resulting zscore is 2.07 which is past the upper .05 rejection region.
So reject by: there is enough evidence to support the claim that more than 55% of U.S. adults regularly watch their local television
Mu SubXbar
the mean of all sample means from samples of size n. This value targets the population mean, , so it is an unbiased estimator
Test Statistic for Testing a Claim About a Mean (with Not Known) requirements
The sample is a simple random sample.
The value of the population standard deviation is not known.
The underlying population is normally distributed or the sample size n > 30
Test Statistic for Testing a Claim About a Mean (with Not Known) use TI-83/84 technology
Use tcdf( for finding P-values and invT( for finding Critical values)
Important Properties of the Student t Distribution
The Student t distribution is different for different sample sizes (see Figure 7-5 in Section 7-4).
The Student t distribution has the same general bell shape as the normal distribution; its wider shape reflects the greater variability that is expected when s is used to estimate ? .
population standard deviation
The Student t distribution has a mean of t = 0 (just as ?
the standard normal distribution has a mean of z = 0).
The standard deviation of the Student t distribution varies with the sample size and is greater than?
1 (unlike the standard normal distribution, which has = 1).
As the sample size n gets larger, the Student t distribution gets _____ to the standard normal distribution.
closer
finding critical values in a t dist
Identify the level of significance
Identify the degrees of freedom, df = n - 1.
Find the critical value(s) using Table A-3 in the row with n - 1 degrees of freedom
left-tailed, use the "Area in One Tail" section and the desired column. Put a _____sign in front of the critical value.
negative
right-tailed, use the "Area in One Tail" section and the desired column. Put a ______sign in front of the critical value
positive
two-tailed, use the "Area in Two Tails" section and the desired column. There will be a ______ critical value.
positive and a negative
Find the critical value t for a left-tailed test given = 0.05 and n = 21
The degrees of freedom are df = n - 1 = 21 - 1 = 20.
Look up = 0.05 column from the "Area in One Tail" section.
Because the test is left-tailed, the critical value is negative.
Find the critical values t and -t for a two-tailed test given = 0.05 and n = 26.
The degrees of freedom are df = n - 1 = 26 - 1 = 25.
Look in the = 0.05 column from the "Area in Two Tails" section.
Because the test is two-tailed, one critical value is negative and one is positive
The Student t critical value is larger (farther to the right), showing that with the Student t distribution, the sample evidence must be_____ before we can consider it to be significant.
more extreme
The original claim contains the condition of equality. You reject the Null hypothesis
there is sufficient evidence to warrent rejection of the claim that...."
This is only the case in which the original claim is rejected
the original claim has equality but you do not reject the null.
there is not sufficient evidence to warrent rejection of the claim that...." "not guilty" verdict
the original claim doesn't contain an equality. you reject the null.
the sample data supports the claim that..." this is the only case where the original claim is supported
the original claim doesn't contain an equality; you don't reject the null.
there is sufficient evidence to support the claim that... (original claim)" "not guilty" vertict
advantages of pooling sample? variances?
Confidence intervals are a little narrower.
The number of degrees of freedom is a little higher.
Hypothesis tests have more power.
Whenever the sample test statistic is not in the rejection region for the hypothesis test using ?=0 as the null? hypothesis, the confidence interval from the sample data will contain?
0. These two methods of reaching a conclusion are equivalent.
Using dependent samples with paired data can help reduce ?
extraneous variation.
The conclusion is the same regardless of if a confidence interval estimate or ?
a hypothesis test is used.
If the sample results cannot easily occur when the null hypothesis is?_____, we conclude that the assumption is not true and reject the assumption.
true
When using the confidence interval method for testing a claim about ? when sigma? is? ____, all three methods are equivalent and produce the same results.
unknown
less than 21,750
sigma > 21750
at most 48 % pay their bills online
P less than or equal to 48%
the null contains equality so the alternative would be
p is greater than .48
how do you calculate the test statistic for:
proportion is equal to .25, a population of 510 has 102 yellow pods.
use 1PropZTest,
Use not equal sign for proportion
N=510
X=102
p=.25
calculate test statistic: less than .30, n=1147 and X =321
Use 1 PropZTest
P< .30
n=1147
x=321
if the significance level is .05 and the alternative is an inequality.
test statistic is -1.35 what is the pvalue?
how do you find the critical values?
find p value by using Normal CDF[-10000,-1.35] =answer.
Multiply this answer by two to represent both tails. This equals = .1770
take .05 divide by two and now subtract from 1. use that number in inversenorm [95] and compute. use both negitive and positiv
the level of significance is .1, find the pvalue and the criitical value if: test statistic is -1.12 and alternative is an inequality
find pvalue by using normalcdf[ -10000,-1.12]= answer
multiply answer by 2 to represent both tails, this equals .2627
to find critical value divide alpha by 2 and subtract from 1. this equals .95. plug this value into inversnorm [ .95] to get : 1.65. Use
if the hypothesis test is only one tailed, how do you compute the critical value?
for example, a significance level or .1 for a right tailed test?
sinply plug significance level into inversnorm, but select the appropriate + or - depending on the tail of test.
Inversnorm(.1)= 1.28, use positive value because it is a right tailed test!
test the claim of P>.4 if the test statistic is 2.11 and the significance level is .05.
Use normal cdf[2.11,10000]= .0174 the area to the right of the test statistic is the pvalue.
for a right tailed test, there will only be one critical value: use the significance level in Inversenorm[.05] this will equal the critical value. Choose the posi
a game had 80% tuned into the game out of 27000 homes. the significance level is .01 and we want to test the claim that more than 72% tuned in. How do you identify the hypothesis', pvalue, test statistic etc?
multiply .80by 27000 to find X, N is 27000. detirnmine this claim is right tailed. "more than" so use >p
use 1PropZtest plug in P, X, and N
when testing gas pumps, 1280 are found to be not accurate. 5664 pumps are accurate. use a .01 significance and test the claim that less than 20% are inaccurate. find critical value too
first add pumps together to get N. (6944)
then identify X (1280) and P. P will be .20
identify the tail: if its less than 20% its left tailed so use :
<P
plug p:,x and n into 1PropZtest.
use inversnorm to find critical value. Its only one tail so do not d
greater than
>
less than
<
how do you use technology to find the p value for a right tailed test with n=11 and a test statistic of t= 1.399
identify n-1 = 10
use tcdf function and plug lower level, upper level and n-1.
tcdf [1.399,9999,10]
1.399 is lower limit, 9999 is upper and 10 is sample size minus one
for a problem that gives you a population mean and sample mean and standard deviation, how do you compute the test statistic and p value?
use Stat,test, T test. Enter Pop mean (mu) sample mean, standard deviation and sample size. Choose appropriate tail or tails and calculate
how do you find the critical value using a t-dist table?
use t- dist. table. look for n-1, on df column. identify which significance level it corresponds to, and identify whether the value needs to be negative or positive, is a right-tailed or left tailed test?
when given values for a sample are given and the question asks you to test the claim that the sample is from a population with certain criteria, how do you compute?
plug sample values into l1, run 1 var stat. Go to stat, test, T-test, and use N, X and standard deviation in formula. Pick the appropriate tail.
a. when asked a question about testing a claim of equal proportions, how do you calculate?
b. if the p value is large what can you conclude?
use a 2 sample proportion, Stat Test 6: 2PropZtest
plug in success and sample size for both samples. Choose tail
b. there is not a significant difference
if the pvalue is less than alpha or the z value is in the critical region there would appear to be a _____ difference between proportion of wins. if the pvalue is .3725 and alpha is .05, is there a significant difference?
significant, no
what requirements are needed for a two population proportion test?
samples must be simple random that are independant. for each the groups there must be 5 success and 5 failures
to test a claim for a 2 prop Ztest by constructing a appropriate confidence interval, you use?
Stat, test, B "2PropZInt"
for confidence %: use alpha. Subtract alpha from 1 to get % and plug into 2PropZint" to get confidence interval
to test the effectiveness of a drug, cholesterol levels are measured in 160 men and 160 women after the treatment, dependant or independant?
the samples are independant because there is no natural pairing between the two samples
for two random samples taken from normally distributed populations, how can you test the claim that the two are from populations with the same mean?
use stat, tests, 4: 2-SampTtest
enter 1st sample N, Sx and mean, plug in second sample's N, Sx, and mean. Choose appropriate tail and calculate
if the pvalue is higher than the significance level, what will you decide?
I will fail to reject the null
what are requirements for testing a claim about population means when population standard deviations are not known and not asumed to be equal?
both samples must be simple random.
both must come from a large >30 or both come from normally distributed populations.
the samples must be independant
what are true statements concerning independant samples?
the pvalue and traditional methods of hypothesis testing result in the same conclusion as the confidence interval method.
what are advantages of pooling sample variences?
confidence intervals are narrower, the number of degrees of freedom is a little higher, hypothesis tests have more power.
two samples are ______ if the sample values are paired
dependant
two samples are ____ if they are not related to or somehow paired or matched with the sample values of the other population
independant.
concerning the mean of the differences between two dependent samples? (matched pairs):If one wants to use a confidence interval to test the claim that mu subd is greater than 0 with a .10 significance? level, the confidence interval should have a confiden
80?%.
concerning the mean of the differences between two dependent samples? (matched pairs): If one has twenty five matched pairs of sample? data, there is a loose requirement that the twenty-five differences appear to be?
from a normally distributed population.
for testing claims about the mean of the dffernces of two dependant samples, how do you enter the values into the calculator?
Go to stat, edit. Plug sample 1 values into l1, Sample 2 values into l2. Go to home screen and select L1 minus L2, Store into L3.
now, go to stat, test, 2, select "data" choose L3 where data is stored. select appropriate tail and the subsequent Xbar will
how do you construct a confidence interval for two dependant samples?
after the data is listed into l3, you can use the T interval. indicate the desired confidence level
principles of making inferences from dependent? samples?
.
The hypothesis test and confidence interval are equivalent in the sense that they result in the same conclusion
There is some relationship whereby each value in one sample is paired with a corresponding value in the other sample
The? t-distribution serv
requirements of testing a claim about the mean of the differences from dependent? samples?
The sample data are dependent.
The samples are simple random samples.
Either the number of pairs of sample data is larger than 30 or the pairs have differences that are from a population having a distribution that is approximately? normal, or both.
n a census of students enrolled in a statistics class, the entire 200 individuals where asked if they felt they deserved an A, 30 stated yes they felt they earned an A. The proportion 30/200 is a
parameter
here are 200 students enrolled in a statistics class, 20 individuals are randomly selected and asked if they felt they deserved an A, 5 stated yes they felt they earned an A. The
proportion 5/20 is a
statistic
Which one is a discrete variable?
(a) Number of balls in an urn
(b) Weight
of a ball in an urn
(c) Diameter of a ball in an urn
(d) Radius of a ball in an urn
Number of balls in an urn
Which one is a continuous variable?
(a) Number of DMF teeth
(b) Number of
patients in a hospital
(c) Number of fish caught in an hour
(d) Weight of fish caught
Weight of fish caught
Which one is at the nominal level of measurement?
(a) Highest degree earned: BA, MA, Ph.D.
(b) Rating of an instructor: Poor, Average,
Excellent
(c) Eye color
(d) Number of students in a classroom
Eye color
Which one is at the ordinal level of measurement?
(a) Eye Color
(b) Rating of an instructor: Poor, Average, Excellent
(c) Temperature in a classroom
(d) Number of students in a classroom
Rating of an instructor: Poor, Average, Excellent
Which one is at the interval level of measurement?
(a) Highest degree earned: BA, MA, Ph.D.
(b) Rating of an instructor: Poor, Average,
Excellent
(c) Temperature in a classroom
(d) Number of students in a classroom
Temperature in a classroom
Which one is at the ratio level of measurement?
(a) Highest degree earned: BA, MA, Ph.D.
(b) Rating of an instructor: Poor, Average,
Excellent
(c) Temperature in a classroom
(d) Number of students in a classroom
Number of students in a classroom
What sampling method is applied when selecting all students in the first row in a classroom?
(a) Cluster
(b) Stratified
(c) Systematic
(d) Convenience
Cluster (all from some)
What sampling method is applied when every tenth student entering a classroom are selected?
(a) Cluster
(b) Stratified
(c) Systematic
(d) Convenience
Systematic (every Kth)
What sampling method is applied when 10 male and 10 female students are randomly selected and combined?
(a) Cluster
(b) Stratified
(c) Systematic
(d) Convenience
Stratified
What sampling method is applied when taking a sample of 10 elementary schools in the State of Florida and including all students in the selected schools to survey?
(a) Cluster
(b) Stratified
(c) Systematic
(d) Convenience
Cluster (all from some)
Which plot can be used for a qualitative variable?
(a) pie chart
(b) histogram
(c) stem-and-leaf plot
(d) box-and
whisker plot
pie chart
Which plot displays raw values of a data set of a quantitative variable?
(a) pie chart
(b) histogram
(c) stem-and-leaf plot
(d) box-and whisker plot
stem-and-leaf plot
Which plot summarizes the five number summary of a data set?
(a) pie chart
(b) histogram
(c) stem-and-leaf plot
(d) box-and whisker plot
box-and whisker plot
Which data set has the smallest variance?
(a) {0,1,1}
(b) {0,1,2}
(c) {0,1,3}
(d) {100, 101, 102}
{0,1,1}
Which data set has the largest mean?
(a) {0,1,1}
(b) {0,1,2}
(c) {0,1,3}
(d) {100,101,102}
{100,101,102}
Which one of the following measures of variation does not change when multiplying 20 to every value of the data set?
(a) Mean
(b) Variance
(c) Range
(d) Coefficient of variation
Coefficient of variation
How many different ways are possible when three positions (supervisor, coordinator, secretary) are filled from a total of 200 candidates?
(a) P200,3
(b) C200,3
(c)200!
(d) 3200
P200,3
Which one is a discrete distribution?
(a) Binomial
(b) Normal
(c) Chi-square
(d) Student's t
Binomial
Which one is a continuous distribution?
(a) Geometric
(b) Poisson
(c) Normal
(d) Binomial
Normal
Which binomial distribution can be well approximated by a normal distribution?
(a) Binomial (n=100, p=0.001)
(b) Binomial (n=100, p=0.99)
(c) Binomial (n=12, p=0.2)
(d) Binomial (n=12, p=0.5)
Binomial (n=12, p=0.5)
Which one is NOT true for a normal distribution?
(a) Symmetric about median
(b) Unimodal
(c) Mean is equal to the standard deviation
(d) Bell (Mound)-shaped
Mean is equal to the standard deviation
Which one is NOT true for a Student's t distribution?
(a) Symmetric about zero
(b) Skewed
(c) As df increases, the distribution gets closer to N(0,1)
(d) Unimodal
Skewed
In an experiment, 100 twins are randomly selected. For each twin, one twin is randomly chosen and given Treatment 1 and the other is given Treatment 2. What do we call
these samples?
(a) Independent two-samples
(b) Paired samples
(c) Stratified samples
(d
Paired samples
Central limit therom
If the samples size n>30 are drawn from a population with the mean mu and standard deviation sigma, then the sampling distribution of samples means will approximate a normal distribution with mean much and standard deviation sigma/sqrtN. If the population
Central limit therom
If the samples size n>30 are drawn from a population with the mean mu and standard deviation sigma, then the sampling distribution of samples means will approximate a normal distribution with mean much and standard deviation sigma/sqrtN. If the population