{Exercise 9.51 (Algorithmic)} A recent issue of the AARP Bulletin reported that
ID: 3156123 • Letter: #
Question
{Exercise 9.51 (Algorithmic)} A recent issue of the AARP Bulletin reported that the average weekly pay for a woman with a high school diploma was $660 (AARP Bulletin, January–February 2010). Suppose you would like to determine if the average weekly pay for all working women is significantly greater than that for women with a high school diploma. Data providing the weekly pay for a sample of 50 working women are available in the WEBfile named WeeklyPay. These data are consistent with the findings reported in the article mentioned above. Please round answers to two decimal places if necessary. Click on the webfile logo to reference the data.
a. State the hypotheses that should be used to test whether the mean weekly pay for all women is significantly greater than the mean weekly pay for women with a high school diploma. H0: Ha:
b. Use the data in the WEBfile named WeeklyPay to compute the sample mean, the test statistic, and the p-value. Sample mean 637.94 Test statistic -.10 p-value
c. Use = .05. What is your conclusion? d. State the rejection rule: Reject H0 if t is the critical value.
Explanation / Answer
t-test For Single Mean
Set Up Hypothesis
Null, H0:average weekly pay for all working women is significantly greater than that for women with a high school diploma U>660
Alternate, H1:average weekly pay for all working women is significantly less than that for women with a high school diploma U<660
Test Statistic
Population Mean(U)=660
Sample X(Mean)=637.77
Number (n)=50
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
| to | =10
Critical Value
The Value of |t | with n-1 = 49 d.f is 1.677
We got |to| =10 & | t | =1.677
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
here we have evedance thataverage weekly pay for all working women is significantly greater than that for women with a high school diploma
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