Teachers' Salaries California and New York lead the list of average teachers' salaries. The California yearly average i $64,421 while teachers in New York make an annual salary of $62,332. Random samples of 40 teachers from each stat yielded the following. California New York Sample mean 64,935 62,425 Population standard 8164 7892 deviation Send data to Excel Use u, for the average teachers' salaries in California. At a= 0.01, is there a difference in means of the salaries? Part: 0 / 5 Part 1 of 5 (a) State the hypotheses and identify the claim. H: (Choose one) ▼ H: (Choose one) ▼ This hypothesis test is a (Choose one) test.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
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Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 1GP
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Teachers' Salaries California and New York lead the list of average teachers' salaries. The California yearly average is
$64,421 while teachers in New York make an annual salary of $62,332. Random samples of 40 teachers from each state
yielded the following.
California
New York
Sample mean
64,935
62,425
Population standard
deviation
8164
7892
Send data to Excel
Use u, for the average teachers' salaries in California. At a = 0.01, is there a difference in means of the salaries?
Part: 0 / 5
Part 1 of 5
(a) State the hypotheses and identify the claim.
Ho: (Choose one) ▼
H¡:
(Choose one) ▼
This hypothesis test is a (Choose one) ▼ test.
Transcribed Image Text:Teachers' Salaries California and New York lead the list of average teachers' salaries. The California yearly average is $64,421 while teachers in New York make an annual salary of $62,332. Random samples of 40 teachers from each state yielded the following. California New York Sample mean 64,935 62,425 Population standard deviation 8164 7892 Send data to Excel Use u, for the average teachers' salaries in California. At a = 0.01, is there a difference in means of the salaries? Part: 0 / 5 Part 1 of 5 (a) State the hypotheses and identify the claim. Ho: (Choose one) ▼ H¡: (Choose one) ▼ This hypothesis test is a (Choose one) ▼ test.
Sample Question
Teachers' Salaries California and New York lead the list of average teachers' salaries. The California yearly average is $64,421 while teachers in New York make an annual salary of
$62,332. Random samples of 40 teachers from each state yielded the following.
California
New York
64,700
62,862
Sample mean
Population standard
deviation
8211
7725
Send data to Excel
Use u, for the average teachers' salaries in California. At a= 0.05, is there a difference in means of the salaries?
(a) State the hypotheses and identify the claim.
(b) Find the critical values.
(c) Compute the test value.
(d) Make the decision.
(e) Summarize the results.
Explanation
(a) State the hypotheses and identify the claim.
The null hypothesis H, is the statement that there is no difference between the means. This is equivalent to u, =u.
The alternative hypothesis H, is the statement that there is a difference between the means. In this case, there is a difference between the means of the salaries. This is equivalent to
The problem asks, "Is there a difference in means of the salaries?" Hence, the claim is the alternative hypothesis H,.
(b) Find the critical values.
From the figure, for a two-tailed test with a=0.05, the critical values are z=t1.96.
H:u=k a-0.10,C.V.--1.28
a= 0.05,C.V.=-1.65
a= 0.10,C.V. -1.28
Summary of
Hypothesis Testing
and Critical Values H:H<k
a= 0.01,C.V. - 2.33
(a) Left-tailed
a-0.10,C.V.- +1.28
H, : u=k
a = 0.05,C.V.= + 1.65
a-0.01,C.V. - +2.33
(b) Right-tailed
a= 0.10,C.V.=±1.65
Ho :-k
a= 0.05,C.V.=±1.96
a= 0.01,C.V.-t2.58
(c) Two-tailed
(c) Compute the test value.
Using the formula for the z test for comparing two means from independent populations, compute the test value:
Transcribed Image Text:Sample Question Teachers' Salaries California and New York lead the list of average teachers' salaries. The California yearly average is $64,421 while teachers in New York make an annual salary of $62,332. Random samples of 40 teachers from each state yielded the following. California New York 64,700 62,862 Sample mean Population standard deviation 8211 7725 Send data to Excel Use u, for the average teachers' salaries in California. At a= 0.05, is there a difference in means of the salaries? (a) State the hypotheses and identify the claim. (b) Find the critical values. (c) Compute the test value. (d) Make the decision. (e) Summarize the results. Explanation (a) State the hypotheses and identify the claim. The null hypothesis H, is the statement that there is no difference between the means. This is equivalent to u, =u. The alternative hypothesis H, is the statement that there is a difference between the means. In this case, there is a difference between the means of the salaries. This is equivalent to The problem asks, "Is there a difference in means of the salaries?" Hence, the claim is the alternative hypothesis H,. (b) Find the critical values. From the figure, for a two-tailed test with a=0.05, the critical values are z=t1.96. H:u=k a-0.10,C.V.--1.28 a= 0.05,C.V.=-1.65 a= 0.10,C.V. -1.28 Summary of Hypothesis Testing and Critical Values H:H<k a= 0.01,C.V. - 2.33 (a) Left-tailed a-0.10,C.V.- +1.28 H, : u=k a = 0.05,C.V.= + 1.65 a-0.01,C.V. - +2.33 (b) Right-tailed a= 0.10,C.V.=±1.65 Ho :-k a= 0.05,C.V.=±1.96 a= 0.01,C.V.-t2.58 (c) Two-tailed (c) Compute the test value. Using the formula for the z test for comparing two means from independent populations, compute the test value:
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