A nationwide survey of working adults indicates that only 50% of them are satisf

Question

A nationwide survey of working adults indicates that only 50% of them are satisfied with their jobs. The president of a large company believes that more than 50% of employees at his company are satisfied with their jobs. To test his belief, he surveys a random sample of 100 employees at the company, and 54 of them report that they are satisfied with their jobs. Can he conclude that more than 50% of employees at the company are satisfied with their jobs? Use a = 0.01 level of significance A. State the null and alternate hypothesis B. Compute the test statistic z C. State conclusion A nationwide survey of working adults indicates that only 50% of them are satisfied with their jobs. The president of a large company believes that more than 50% of employees at his company are satisfied with their jobs. To test his belief, he surveys a random sample of 100 employees at the company, and 54 of them report that they are satisfied with their jobs. Can he conclude that more than 50% of employees at the company are satisfied with their jobs? Use a = 0.01 level of significance A. State the null and alternate hypothesis B. Compute the test statistic z C. State conclusion A. State the null and alternate hypothesis B. Compute the test statistic z C. State conclusion

Explanation / Answer

P= 0.5 ,Q =1-P = 1-0.50= 0.50 , x= 54, n= 100 and p= x/n= 0.54

NULL HYPOTHESIS H0: P= 0.5

ALTERNATIVE HYPOTHESIS HA: P>0.5 (RIGHT TAILED)

level of significance= 0.01

Under NULL HYPOTHESIS H0, test statistic is

Z= p-P/SQRT(P*Q/n)

Z= 0.54-0.5/SQRT(0.5*0.5/100)

Z= 0.04/0.05 = 0.8

CRITICAL VALUE OF Z AT 0.01 LEVEL OF SIGNIFICANCE IS 2.33

CONCLUSION: SINCE CRITICAL VALUE IS GREATER THAN CALCULATED VALUE OF Z STATISTIC AT 0.01LEVEL OF SIGNIFICANCE, WE DO NOT REJECT NULL HYPOTHESIS AND CONCLUDE THAT ONLY 50% ADULTS ARE SATISFIED WITH THEIR JOBS.

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