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.

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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
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.
 
Enter your answer in each of the answer boxes.
 
 
 
 
 
 
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