The ___________ the sample size, the smaller the sampling error tends to be in estimating a population mean, ?, by a sample mean, x .
larger
The error that results from using sampling to estimate information regarding a population is called _____________.
sampling error
What are the two conditions sufficient to assume that the distribution of sample means will be (approximately) NORMALLY distributed?
a. if the original variable is approximately normally distributed; b. if the sample size is large enough (our sample size must be 30 or larger)
A(n) _____ for an unknown parameter consists of an interval of numbers. This estimate may or may not contain the value of the parameter being estimated.
confidence interval
The _____ represents the expected proportion of intervals that will contain the parameter if a large number of different samples is obtained.
level of confidence
For a fixed sample size, the greater the confidence level, the ____ the length of the confidence interval.
greater
For samples where the standard deviation is unknown, what distribution is used for determining confidence intervals?
t-distribution
The null hypothesis for a hypothesis test should always contain what symbol (=, <, >)? ____________ .
0
The ___________________ represents the maximum number of standard deviations the sample mean can be from before the null hypothesis is rejected.
critical value
The set of all values such that the null hypothesis is rejected is called the __________________________ .
rejection region or critical region
Two events are ____ (mutually exclusive) if they have
disjoint, no outcomes in common
0! equals
1
1! equals
1
how do you find the mean when given x and p(x) in a table
multiple values in both columns, and then add up all the sums to get the mean
how do you find the standard deviation when given x and p(x) in a table
1. add 2 columns (c and d): x squared, and x squared times p(x)
2. add column d's values
3. square the mean, and subtract it from column d's sum
4. take the square root
what do the x, n, and p stand for?
x= number of successes
n=number of trials
p=probability of success
The ACT is a college entrance exam. The mean ACT score of all students who took the exam in 2007 was 21.2, with a standard deviation of 4.9. Research seems to indicate that students score better on the ACT when they take the core mathematics curriculum. a
H0: ?=21.2 (null)
Ha: ? > 21.2 (alt)
right tailed test
If you want to prove that the mean is higher than the population mean
left tailed test
If you want to prove that the mean is smaller than the population mean
two tailed test
if you want to see if the mean is different from the mean in either direction
null is always
h0
the null test always includes an
equal sign
the alt. hypothesis is what we are
trying to prove
Type 1 error
null hypothesis is correct
type 2 error
alt. hypothesis is correct
how would you figure out these two questions: Does the answer in part c suggest that completing the core mathematics curriculum improves ACT scores? e) Given your answer in part d, if an error has been made, what type must it be?
if the test value is greater than the critical value, the null hypothesis will be rejected. Therefore, the alt. hypothesis is correct (type 1 error)
if the test value is less than the critical value, there is not sufficient evidence to prove the alt. hypo
p(x less than or equal to a)
a + .5
p(x greater than or equal to a)
a - .5
p(x is between a and b)
a - .5 and b + .5
If df = ?, then t? =
z?
how do you get df
n-1
?=
the percent left from the confidence level
t= add an extra zero
z= don't add an extra zero
level of confidence of 90% has a critical value of
1.645
level of confidence of 95% has a critical value of
1.96
level of confidence of 98% has a critical value of
2.33
level of confidence of 99% has a critical value of
2.575
if the level of significance is 0.05, then the right tailed critical value would be
1.645
For the t-distribution, when determining confidence intervals the number of degrees of freedom is
equal to:
n - 1.