Which of the following is a descriptive statistic?
All of these choices are correct.
Suppose the growth chart at a pediatrician's office is not hung correctly such that it measures children 2 inches taller than their actual height. If the heights of ten children are recorded, which of the following is a true statement?
The measurements of the heights that were recorded represent a data acquisition error.
Statistical studies in which researchers control variables of interest are
experimental studies.
In production, which of the following indicates "underfilling"?
Underfilling occurs when a plotted value is below the chart's lower control limit.
A characteristic of interest for the elements is called a(n)
variable.
A sample of 100 individuals in a town was asked how much they paid in property tax per year. On the basis of this information, the reporter states that the average property tax bill of all residents of the town is $1500. This is an example of
statistical inference.
A local grocery store recorded the amount spent for a sample of 50 customers who purchased groceries. Which of the following is not a true statement?
This is an experimental study.
A data set that is collected at the same or approximately same point in time would be
cross-sectional data.
The table is an example of
cross-tabulation data
A hospital has noted that on average there are 35 emergency room visits per month involving children. The average number of visits is an example of
a descriptive statistic.
Consider the following data summary.
a histogram.
Which of the following variables is quantitative?
Weight of a package
Which of the following professionals frequently use statistical techniques to provide forecasts about the future of the economy?
Economists
Which of the following disciplines has contributed the least to the development of data mining procedures?
Psychology
What does the term "statistics" refer to?
Statistics is the art and science of collecting, analyzing, presenting and interpreting data.
Which of the following is an example of an observational study?
All of these choices are examples of observational studies.
In a sample of 200 people who own a house, 180, or 90%, also own two or more vehicles. The 90% is an example of
a descriptive statistic
Using data containing errors is always better than using no data at all.
False
A survey of 40 students at an elementary school found that the average number of tardy days per semester was 15. The 15 is an example of
both choices "quantitative data" and "a descriptive statistic" are correct.
Local residents were surveyed for their satisfaction with the local government. The responses were recorded as follows: 0-not satisfied, 1-somewhat dissatisfied, 2-satisfied, 3-very satisfied. The variable recorded is an example of what type of variable?
a variable measured on the ordinal scale.
The city would like to conduct a study of the opinions of its residents on an upcoming election. Since it would be too costly to call every person who is registered to vote in the city they decide to call every 15th person in the records database. Which o
The study is a sample survey.
Data mining is the process of uncovering hidden information that can be used to
predict
Consider the following data as well as the corresponding stem-and-leaf display on the annual property taxes for eight residents of a city.
100
Which of the following statements is true with respect to bar charts?
A bar chart can be used for a data set with a relatively small number of possible categories.
The sum of the frequencies for all classes will always equal
the number of elements in a data set
Information on the number of new teachers hired in a school district for each of 4 years is given in the table below.
The percent frequency of new hires in 1998 is:
40%
Which of the following cannot be conveyed using a stem-and-leaf display? (Assume that the entire values are used in creating the stem-and-leaf display.)
The order in which the observations were taken
The number of sick days taken (per month) by 150 factory workers is summarized below.
The cumulative frequency for the class 11 - 15 is:
145
Consider the scatter diagram below.
What type of relationship is shown the number of students and average score?
a positive relationship
The following is a summary of the number of hours spent per work day involved in meetings for a sample of 50 people.
What is wrong with the relative frequency distribution?
The relative frequencies do not add to 1.
The relative frequency of a class:
is equal to the frequency of the class divided by the total number of observations, n.
Consider the following graphical summary.
This is an example of a
pie chart
In a cumulative relative frequency distribution, the last class will have a cumulative relative frequency equal to:
1
A survey of 400 college seniors resulted in the following crosstabulation regarding their undergraduate major and whether or not they plan to go to graduate school.
What percentage of the undergraduates surveyed are majoring in Engineering?
38%
Suppose a sample of 150 individuals was taken. Their gender and their preferred computer manufacturer was noted. Partial results of the study follow in a cross tabulation of column percentages.
If 80 of those in the study prefer Apple computers, how many
64
Consider the portion of a stem-and-leaf display shown below. If the leaf unit is 100 what is the value of the data point associated with a leaf value of 9? 8 | 2 5 9
8900
The numbers of miles from their residence to their place of work for 120 employees is shown below.
The relative frequency of employees who drive 10 miles or less to work is:
0.71
If a negative relationship exists between two variables, x and y, which of the following statements is true?
As x increases y decreases.
What types of variables can be displayed by a scatter diagram?
Two quantitative variables
If several frequency distributions are constructed from the same data set, the distribution with the largest class width will have the:
fewest classes
Which of the following is the correct formula for computing the population mean for grouped data?
In 2000, the average hours of television watched weekly in a household was 5 with a standard deviation of 1.43. In 2002, average hours of television watched weekly in a household was 8 with a standard deviation of 3.12. Which of the following statements i
The number of hours is more variable in the year 2002
If the value of the covariance is positive, then the values with the greatest influence will be located in which quadrants?
I and III
Which of the following is a possible reason for an outlier in a data set?
All of these choices are possible reasons for an outlier.
Which of the following pairs of variables cannot be studied using covariance or correlation?
Type of car owned and yearly income
What is the range of income for five randomly chosen individuals aged 22 to 24? The data are $72,500, $26,200, $17,900, $36,000, $52,100.
$54,600
Suppose a study of two variables, cost of a product (x) and number of products sold (y), gave the following summary:
rxy = .81
When computing the sample mean for grouped data, the size of the sample is represented by:
n
According to the Chebychev's Theorem, at least what percentage of the observations in data set will lie within three standard deviations of the mean?
89%
Find the z-score for a value of 104 when the mean is 88 and the variance is 10.
5.1
Which of the following statements is correct with respect to the distribution of gallons shown in the box plot below?
The interquartile range is approximately 32.
Which of the following represents the data point that occurs most frequently in a set of observations?
Mode
Measures of location and dispersion should be computed from grouped data rather than from individual data values:
only when individual data values are unavailable
What can be concluded from the scatter diagram below for the two variables, years of education and unemployment rate?
The covariance will be negative.
Suppose the number of personal days an employee uses per year has a mean of 8 and a standard deviation of 2. What percent of the data values will be within 2 standard deviations of the mean if the distribution is bell-shaped?
at least 95%
If a data set has an odd number of observations, the median
is the value of the middle item when all items are arranged in ascending order.
A student at a local college just completed 14 credit hours. His grade report is presented below.
The university uses a 4-point grading system, i.e., A = 4, B = 3, C = 2, D = 1, F = 0. What is the student's grade point average for this semester?
2.27
How would the shape of the histogram shown below be described?
The shape is skewed left
Using the following data set of monthly rainfall amounts recorded for ten randomly selected months in a two year period, what is the five-number summary? Sample data (in inches): 2, 8, 5, 0, 1, 5, 7, 5, 2, 0.5
0, 1, 3.5, 5, 8
Suppose a sample of 45 measurements gave a data set with a range of -8 to -22. The standard deviation of the measurements:
must be at least zero
If the sample standard deviation for the number of new vehicles sold per month for a sample of 6 car dealerships is 4.2, what is the variance for this set of data?
17.6
The correlation coefficient:
can be negative
The following is the frequency distribution for the ages of a sample of senior citizens who attend a local bingo night. What is the standard deviation for this data set?
5.57
The 25th percentile is:
20
Find the average miles per gallon for ten different vehicles using the data given below. Miles per gallon: 35, 12, 22, 20, 18, 19, 18, 25, 31, 28
22.8
The five-number summary for a set of data is 15, 24, 38, 41, 55. What is the mean for this data set?
The mean cannot be determined from the information given.
When constructing a box plot, outliers are those data points that lie beyond which of the following?
Q1 - 1.5(IQR) or Q3 + 1.5(IQR)
If the variance of a data set is correctly computed with the formula using n - 1 in the denominator, which of the following is true?
The data set is a sample
The median of a data set is represented by the:
50th percentile
What is the five-number summary?
6.00, 6.43, 7.05, 7.45, 7.60
Which of the following is not true when assigning probabilities to each of n experimental outcomes in a sample space?
P(E1) - P(E2) + ... + P(En) = 0
Two parts are selected for inspection. Each part is classified as D (defective) or N (nondefective). What is the sample space for this experiment?
S = {(D,D),(D,N),(N,D),(N,N)}
Ten individuals attend a group ski lesson. Two individuals are selected from the group lesson to receive private lessons for a 15-minute period. In how many ways can the two individuals be selected if order is not important?
45
A local retail store recorded the number of customers who entered the store between 9 and 11 am for five consecutive weekdays.
What is the probability that on a given day three customers entered the store between 9 and 11 am?
.4
What is the probability of randomly drawing a red ball from a bag that contains 2 red balls, 5 blue balls, 1 white ball, and 3 purple balls?
2/11
If there are two traffic lights between your house and your office, what is the probability that you will have two green lights on the way to work? Assume that each element of the sample space is equally likely to occur. Hint : The sample space is S = {GG
0.25
Which of the following defines the event that an even number appears on the upper face when a die is rolled?
E = {2, 4, 6}
The form of payment at a local retail store was recorded for a survey of 100 customers. The results are shown in the table below.
What is the probability that a randomly selected customer does not use a type of credit card to make a purchase?
.32
In a survey of customers at a music store the age of the person was recorded and is shown below. What is the probability that a randomly chosen customer is between the ages of 15 and 19?
0.20
If a fair die is rolled and the number of dots is noted, what is the probability that there will be fewer than 4 dots on the face of the die?
1/2
Which of the following represents the general addition law?
P(A?B) = P(A) + P(B) - P(A?B)
If A and B are mutually exclusive events with P(A) =.45 and P(B) =.05, what is the P(A ? B)?
.50
What is represented by the shaded area in the figure below?
R?Q
Let F be the event that a customer is dissatisfied with the food at a restaurant and let S be the event that a customer is dissatisfied with the service. If P(F)=.15, P(S)=.40 and P(F?S)=.10, what is the probability that a customer is dissatisfied with ei
0.45
If a television fails with probability P(F) =.09, what is the probability that the television does not fail?
.91
Which of the following is the multiplication rule for the probability that two events occur simultaneously or in sequence when the two events are not independent?
P(U?V) = P(V)P(U|V)
A group of children were asked whether they would prefer to have a cat or dog for a pet. The table below gives the data collected.
What is the marginal probability for "dog"?
.44
Suppose a person will purchase a new vehicle within the next six months with probability equal to .35. If the probability that a person will receive a raise within the next six months.20, what is the probability that a person purchases a new vehicle and r
.07
In a random sample of 200 students 55% indicated they have full-time jobs while the other 45% have part-time jobs. Fifty of the 90 male students surveyed have a full-time job and 60 of the females surveyed have a full-time job. What is the probability tha
.56
A string of lights contains 3 lights. The lights are wired in series, so that if any light fails the whole string will go dark. Each light has probability.10 of failing during a 2-year period. If the lights fail independently of each other, what is the pr
.729
Prior probabilities of events are:
initial estimates of the probabilities.
The prior probabilities for events A1, and A2 are P(A1) =.25, and P(A2) =.75. The conditional probabilities of event B given A1, and A2 are P(B | A1) =.45, and P(B | A2) =.30. Using Bayes' theorem, what is the posterior probability P(A2 | B)?
0.6667
Females account for 65% of sales at a major retailer. Assume the probability of a customer being female is .65. The probability that a purchase made by a female exceeds $100 is .32 and the probability that a purchase made by a male exceeds $100 is .6. Sup
0.50
Given that z is a standard normal random variable, what is the value of z if the area to the right of z is 0.9370?
- 1.53
A production line fills 64 ounce bottles of juice uniformly according to the following probability density function
.4
What is the P(10�x�30) for a uniform random variable defined on the interval 0 to 40?
.5
Let x be a uniform random variable on the interval 1�x�6. What is the standard deviation of x?
1.44
The time it takes to completely clean an office building follows an exponential distribution with a mean of 135 minutes. What is the probability of cleaning an office building in 135 minutes or less?
.6321
Suppose the flight time between Atlanta and Salt Lake City is uniformly distributed on the interval from 220 to 250 minutes. The expected flight time (in minutes) is:
235
A small business owner determines that her revenue during the next year should be approximately normally distributed with a mean of $425,000 and a standard deviation of $130,000. What is the probability that her revenue will exceed $600,000?
.0885
The lodge at a ski resort has 50 suites. In the winter months, the occupancy rate for the suites is approximately 90%. What is the probability that at least 80% of the suites are occupied on a given day?
.9952
Suppose a preliminary screening is given to prospective student athletes at a university to determine whether they would qualify for a scholarship. The scores are approximately normal with a mean of 85 and a standard deviation of 20. If the range of possi
50%
When using the normal approximation to the binomial, what is the standard deviation for a binomial probability distribution with p =.3 and n = 145?
5.52
Which of the following represents the mean of the normal distribution used to approximate a binomial distribution?
Suppose that the lifetime of batteries in a flashlight is exponentially distributed with a mean of 35 hours. What is the probability that the batteries will last between 25 and 30 hours?
.0651
what is the mean of x for the exponential distribution
2
The lodge at a ski resort has 50 suites. In the winter months, the occupancy rate for the suites is approximately 90%. What is the probability that 45 or fewer rooms are occupied on a given day?
.5000
The normal distribution is symmetric about:
the mean
If the random variable X is distributed normally with a mean of 0 and a standard deviation of 1, which of the following probabilities is not correct?
P(x = 0) =.50
Which of the following distributions is not symmetric?
Exponential
Consider the continuous random variable x, which has a uniform distribution over the interval from 110 to 150. The probability that x will take on a value between 120 and 125 is:
.125
If a random sample of size n = 20 is taken from a normal distribution with a mean , which of the following would be an unbiased estimator for ?
x?
A university is interested in the average age of its students. a simple random sample of 30 students was selected. the following descriptive statistics for their ages were computed: x? = 20.8 and s? = 8.4. What is a point estimate of the population standa
2.9
If the sample size is increased, the standard error of the sampling distribution of x? will
Decrease
Suppose a random sample of 20 observation is taken from an infinite population. The sampling distribution of pbar is
approximately normal if np � 5 and n(1 - p)� 5
Suppose candidate A for a town council seat receives 43% of the votes in an election. As voters leave the polls they are asked who they voted for. What is the probability that less than 40% of the 80 voters surveyed indicate they voted for candidate A? As
.2939
The sample mean, x? , obtained from repeated samples of the same size from a population is
a random variable.
Residents who own a house in a particular city were divided into 15 groups based on the location of their house. A random sample of ten residents from each of the 15 groups was selected to be interviewed. What type of sampling plan is being used?
Stratified random sampling
A simple random sample of 8 high school student's ACT scores gave the following data
27 30 20 29 28 36 34 31
What is a point estimate for , the mean test score for the population?
29.38
A population of size 320 has a proportion equal to .60 for the characteristic of interest. What are the mean and the standard deviation, respectively, of the sample proportion for samples of size 12?
.60 and.14
Starting salaries of a sample of five management majors along with their genders are shown below.
If we select simple random samples of size 2 from the given data, what is the probability of any of the five employees being selected first?
0.20
Given the sampling distribution of the sample mean shown here, which of the following values is a reasonable estimate for the population mean?
300
A sample of 240 is selected from a finite population of 500. If the standard deviation of the population is 44, what is the standard error of the sample mean?
2.05
Suppose the salaries of university professors are approximately normally distributed with a mean of $65,000 and a standard deviation of $7,000. If a random sample of size 25 is taken and the mean is calculated, what is the probability that the mean value
0.2005
Which of the following is an unbiased point estimator?
x? is an unbiased estimator of ?
A dealership is interested in the population proportion of new vehicle purchases that are gold in color. Which of the following represents the sample statistic of interest?
pbar
Supposed 8 out of 26 cars that pass a radar station are exceeding the speed limit. if the population proportion of cars that exceed the speed limit is .42, what is the value of pbar?
.31
The CEO of a large corporation is interested in the average salary of all managers for his large corporation. A sample of 500 managers found the average salary to be $56,500. Which of the following statements is correct?
The average salary for the 500 managers can be used to estimate the average salary for all managers.
A wildlife management organization is interested in estimating the number of moose in a particular region. Organization employees divide the region into ten sections and randomly select four sections to survey the number of moose present. What sampling me
Cluster sampling
The proportion of students at a university who pass a biology class is p =.86. If 50 students are randomly selected, what is the probability that at least 75% of them have passed the class?
.9875
A sample chosen by stratified random sampling involves:
selecting a simple random sample from each of a given number of strata formed from the elements in the population.
A simple random sample of size 5 from an infinite population is to be selected. Each possible sample should have:
the same probability of being selected
The population mean is represented by the symbol:
?
The number of simple random samples of size 20 that can be selected from a finite population of size 25 is:
53,130
Which of the following estimates is an unbiased estimator for ?^2
The sampling distribution describes the:
long-run behavior of a statistic.
When the selection of one element from the population influences the selection of another element, the sample:
contains selection bias
For which of the following sampling methods can the sampling distribution of the sample statistics generally be identified?
All of these choices are correct.
The symbol p typically represents a:
proportion.
What is the t value for t.05 and 7 degrees of freedom?
1.895
The manager of a retail store has taken a random sample of 100 customers. The average amount spent by these 100 customers was $75. It is known that the standard deviation of the amount spent is $8.20. If the confidence coefficient is increased from .90 to
will remain unchanged.
A random sample of 10 employees was taken. The average age in the sample was 42 with a variance of 25. Assuming the ages are normally distributed, the 95% confidence interval for the population average age is:
38.42 to 45.58
Which of the following must be decided by the researcher when computing the minimum sample size for an interval estimate of ? or p?
Margin of error
A random sample of 35 items is selected from a population that is not normally distributed and whose standard deviation is not known. if x? = 300 and s = 80, which of the following distributions should be used to compute an interval estimate for ?
A t distribution with 34 degrees of freedom.
The z value for a 99% confidence interval estimation is:
2.57
In which of the following situations should the t distribution be used?
When the population standard deviation is unknown
A 90% confidence interval for a population proportion is determined to be 0.75 to 0.85. If the level of significance is decreased, the interval for the population proportion:
becomes wider
A 90% confidence interval and a 96% confidence interval are computed from the same set of data. Which of the following statements is correct?
The 96% confidence interval is wider
A university recruiter would like to determine the proportion of high school students who plan to apply for financial aid when attending college. She surveys 114 current high school seniors who plan to attend college and finds that 98 plan to apply for fi
.7963 to .9237
Which of the following values of p should be used to compute the sample size that guarantees all estimates of proportions will meet the margin of error requirement?
.50
Which of the following is not required when computing the sample size for an interval estimate of the population mean?
Population mean
It is known that the variance of a population equals 169. With a .90 probability, how large of a sample would have to be taken to provide a margin of error of 10 or less?
5
What sample size should be used if we would like to estimate the mean income of the residents of an apartment complex with 95% confidence? We would like to be accurate to within $2000 and we will assume the population is normally distributed with a standa
17
A random sample of 10 varieties of yogurt was selected. The average calories per serving for these yogurts is x? = 90. Assuming that ? = 5, find a 95% confidence interval for the mean calories, ?, in a serving of cereal.
86.9 � 93.1
For which of the following situations would a Type II error be committed?
When a true alternative hypothesis is mistakenly rejected.
suppose a random sample of 30 bundles of wood had the following statistics for the weight of the bundles: x? = 25.4, s = 4.6. What is the test statistic for testing
t = 1.67 with degrees of freedom = 29
Which of the following statements is false?
The null hypothesis always includes an inequality statement.
Which of the following describes the situation in which the null hypothesis has been rejected when the alternative hypothesis is true in a hypothesis test?
The correct decision has been made.
A student believes that less than 50% of students at his college receive financial aid. A random sample of 120 students was taken. Sixty-five percent of the students in the sample receive financial aid. Test the hypothesis at the 2% level of significance.
.999; Do not reject H0
When performing a one-tailed (>) test with a sample size of 20 and ? unknown, the null hypothesis will be rejected at a 5% level of significance if the test statistic is:
greater than 1.729
If the sample size increases for a given level of significance, the probability of a Type II error will:
decrease.
A machine produces parts on an assembly line for an automotive manufacturer. If a part is defective it must be scrapped. Every hour, the manager takes a random sample of 15 parts to test whether the process is "out of control" (i.e. to test whether the av
A Type I error for this situation would be to incorrectly conclude that the process is out of control.
What type of test is being performed if the rejection area is located in both tails (upper and lower) of the sampling distribution?
two-sided (�)
Which of the following statements is true with respect to hypothesis testing?
The p-value approach and critical value approach will always provide the same hypothesis-testing conclusion.
What is the value of z in the sample size formula for a one-tailed hypothesis test about a population mean,
1.04
In the past, 25% of the town residents participated in the school board elections. The town officials recently undertook an extensive campaign to encourage registered voters to participate in the election process. They are interested in determining whethe
H0: p �.25 Ha: p >.25
When the hypotheses H0: ? = 12 and Ha: ? � 12 are tested at a significance level ? =.01, the null hypothesis will be rejected if the test statistic z is:
either < -z.005 or > z.005
For which of the following situations would a Type II error be committed?
when a true alternative hypothesis is mistakenly rejected
Which of the following represents a Type I error for the null and alternative hypotheses H0: ? � $3,200 and Ha: ? > $3,200, where ? is the average amount of money in a savings account for a person aged 30 to 40?
A Type I error would occur if we reject H0 and conclude that the average amount is greater than $3,200 when in fact the average amount is $3,200 or less.
Consider the following hypothesis test.
H0: ? = 8 Ha: ? � 8
The population standard deviation is 2. Use ? =.01. How large a sample should be taken if the researcher is willing to accept a .05 probability of making a Type II error when the actual populatio
18
What is the probability of a Type II error for the following test of hypotheses, given that ? = 23.315?
.4840
Joe believes that the average battery life of a vehicle is equal to 9 years. A sample of 5 vehicles was taken and the following data on battery lives was obtained. Assume the distribution of the population is normally distributed.
What is the value of the
- 4.54
If the power of a statistical test is equal to .9820, what is the probability of a Type II error for the same test?
.018
A local car dealer claims that the percent of customers that are female is more than one-half. Using the sample information reported below, carry out a test of this statement. Use a .05 level of significance.
What is the test statistic?
2.14
A computer manufacturer claims its computers will perform effectively for more than 5 years. Which pair of hypotheses should be used to test this claim?
H0: ? � 5 Ha: ? > 5
A researcher should take action if the null hypothesis is rejected when:
All of these choices are correct
The manager of a major retail store has taken a random sample of 25 customers. The average sale was $52.50. The population standard deviation is known to be $6.10. The manager would like to determine whether or not the mean sales by all customers are sign
.02