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 $680 (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: μ - Select your answer -greater than 680greater than or equal to 680equal to 680less than or equal to 680less than 680not equal to 680 Ha: μ - Select your answer -greater than 680greater than or equal to 680equal to 680less than or equal to 680less than 680not equal to 680 b. Use the data in the WEBfile named WeeklyPay to compute the sample mean, the test statistic, and the p-value. Sample mean Test statistic p-value - Select your answer -Less than .005Between .005 and .01Between .01 and .025Between .025 and .05Between .10 and .20More than .2 c. Use α = .05. What is your conclusion? - Select your answer -The mean weekly pay for all women is higher than that for women with only a high school diploma.The mean weekly pay for all women is lesser than that for women with only a high school diploma. d. State the rejection rule: Reject H0 if t is - Select your answer -greater than or equal togreater thanless than or equal toless thanequal tonot equal to the critical value.
																																																																	Weekly Pay
																																																																	582
																																																																	333
																																																																	759
																																																																	633
																																																																	629
																																																																	523
																																																																	320
																																																																	685
																																																																	599
																																																																	753
																																																																	553
																																																																	641
																																																																	290
																																																																	800
																																																																	696
																																																																	627
																																																																	679
																																																																	667
																																																																	542
																																																																	619
																																																																	950
																																																																	614
																																																																	548
																																																																	570
																																																																	678
																																																																	697
																																																																	750
																																																																	569
																																																																	679
																																																																	598
																																																																	596
																																																																	557
																																																																	657
																																																																	617
																																																																	1230
																																																																	648
																																																																	760
																																																																	804
																																																																	675
																																																																	736
																																																																	565
																																																																	587
																																																																	565
																																																																	687
																																																																	498
																																																																	712
																																																																	533
																																																																	424
																																																																	772
																																																																	691

Answer 1

a)

Ho :   µ =   680
Ha :   µ >   680

b)

sample std dev ,    s = √(Σ(X- x̅ )²/(n-1) ) =   148.4694                  
Sample Size ,   n =    50                  
Sample Mean,    x̅ = ΣX/n =    637.9400                  
                          
degree of freedom=   DF=n-1=   49                  
                          
Standard Error , SE = s/√n =   148.4694   / √    50   =   20.9967      
t-test statistic= (x̅ - µ )/SE = (   637.940   -   680   ) /    20.997   =   -2.003

p value : More than .2

c)

p-value>α, Do not reject null hypothesis   

The mean weekly pay for all women is lesser than that for women with only a high school diploma.

d)

critical t value, t* =        1.677   [Excel formula =t.inv(α/no. of tails,df) ]

reject Ho, if t > 1.677