A teacher's union would like to see if there is a difference in the variability of the salaries earned by high school teachers in one county as compared to another. A random sample of teacher salaries from each county was selected, and the standard deviation of each sample was calculated. Use the information given below to complete parts a and b. County 1 County 2 Sample standard deviation $3,500 $2,900 Sample size 30 30 a. Using α=0.10, determine if there is a difference in the variability of the salaries in the two counties. Identify the null and alternative hypotheses. H0: σ21 ▼ equals= less than or equals≤ greater than or equals≥ σ22 H1: σ21 ▼ less than< not equals≠ greater than> σ22 Calculate the appropriate test statistic. The test statistic is nothing. (Round to two decimal places as needed.) Determine the appropriate critical value(s). The critical value(s) is(are) nothing. (Round to three decimal places as needed. Use a comma to separate answers as needed.) Do not reject Do not reject Reject the null hypothesis. There is sufficient insufficient sufficient evidence that the population variance for County 1 is equal to equal to greater than different from less than the population variance for County 2. b. Use technology to find the p-value and interpret the result. The p-value is nothing. (Round to three decimal places as needed.) Since the p-value is greater than less than greater than α=0.10, reject reject do not reject the null hypothesis. There is insufficient sufficient insufficient evidence to conclude that the population variance for County 1 differs from is less than equals differs from is greater than County 2.
A teacher's union would like to see if there is a difference in the variability of the salaries earned by high school teachers in one county as compared to another. A random sample of teacher salaries from each county was selected, and the standard deviation of each sample was calculated. Use the information given below to complete parts a and b. County 1 County 2 Sample standard deviation $3,500 $2,900 Sample size 30 30 a. Using α=0.10, determine if there is a difference in the variability of the salaries in the two counties. Identify the null and alternative hypotheses. H0: σ21 ▼ equals= less than or equals≤ greater than or equals≥ σ22 H1: σ21 ▼ less than< not equals≠ greater than> σ22 Calculate the appropriate test statistic. The test statistic is nothing. (Round to two decimal places as needed.) Determine the appropriate critical value(s). The critical value(s) is(are) nothing. (Round to three decimal places as needed. Use a comma to separate answers as needed.) Do not reject Do not reject Reject the null hypothesis. There is sufficient insufficient sufficient evidence that the population variance for County 1 is equal to equal to greater than different from less than the population variance for County 2. b. Use technology to find the p-value and interpret the result. The p-value is nothing. (Round to three decimal places as needed.) Since the p-value is greater than less than greater than α=0.10, reject reject do not reject the null hypothesis. There is insufficient sufficient insufficient evidence to conclude that the population variance for County 1 differs from is less than equals differs from is greater than County 2.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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A teacher's union would like to see if there is a difference in the variability of the salaries earned by high school teachers in one county as compared to another. A random sample of teacher salaries from each county was selected, and the standard deviation of each sample was calculated. Use the information given below to complete parts a and b.
|
County 1
|
County 2
|
---|---|---|
Sample standard deviation
|
$3,500
|
$2,900
|
|
30
|
30
|
a. Using
α=0.10,
determine if there is a difference in the variability of the salaries in the two counties.Identify the null and alternative hypotheses.
H0:
σ21
σ22
▼
equals=
less than or equals≤
greater than or equals≥
H1:
σ21
σ22
▼
less than<
not equals≠
greater than>
Calculate the appropriate test statistic.
The test statistic is
nothing.
(Round to two decimal places as needed.)
Determine the appropriate critical value(s).
The critical value(s) is(are)
nothing.
(Round to three decimal places as needed. Use a comma to separate answers as needed.)
Do not reject
Do not reject
Reject
sufficient
insufficient
sufficient
equal to
equal to
greater than
different from
less than
b. Use technology to find the p-value and interpret the result.
The p-value is
nothing.
(Round to three decimal places as needed.)
Since the p-value is
the null hypothesis. There is
evidence to conclude that the population variance for County 1
County 2.
greater than
less than
greater than
α=0.10,
reject
reject
do not reject
insufficient
sufficient
insufficient
differs from
is less than
equals
differs from
is greater than
Enter your answer in each of the answer boxes.
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