Question

Question #2    Hypothesis Testing

A recent issue of AARP Bulletin reported that the average weekly pay for a woman with a high school diploma was $520. 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 Excel file (Weekly Pay). Formulate the null and alternative hypotheses and conduct the appropriate test. What is your conclusion?

Weekly Pay

582         320       290     542     678       596        760         565        772

333         685       800     619     697       557        804         687        691

759         599       696     950     750       657         675        498

633         753       627     614     569       617         736        712

629         553       679     548     679      1230        565        533

523         641       667     570     598       648         587        424

Answer 1

Solution:

Given: A recent issue of AARP Bulletin reported that the average weekly pay for a woman with a high school diploma was $520.

That is: Population mean =

We have to test if the average weekly pay for all working women is significantly greater than that for women with a high school diploma.

That is we have to test:

We are given that the data of weekly pay for a sample of 50 working women.

Thus we use following steps:

Step 1) State H0 and H1:

Vs

Step 2) Find test statistic:

Since population standard deviation is unknown , we use t test statistic.

where

Thus we need to make following table:

x	x^2	x	x^2	x	x^2	x	x^2
582	338724	800	640000	750	562500	736	541696
333	110889	696	484416	569	323761	565	319225
759	576081	627	393129	679	461041	587	344569
633	400689	679	461041	598	357604	565	319225
629	395641	667	444889	596	355216	687	471969
523	273529	542	293764	557	310249	498	248004
320	102400	619	383161	657	431649	712	506944
685	469225	950	902500	617	380689	533	284089
599	358801	614	376996	1230	1512900	424	179776
753	567009	548	300304	648	419904	772	595984
553	305809	570	324900	760	577600	691	477481
641	410881	678	459684	804	646416
290	84100	697	485809	675	455625

Thus we get:

Thus

Step 3) Find t critical value:

df = n -1 = 50 - 1 = 49

Look in t table for df = 49 or if it is not listed , then look for its previous df

and at one tail area = 0.05 and find corresponding t critical value.

One tail area , since this is one tailed test and level of significance is not given , so we use default level of significance = 0.05.

Thus we get:

df = 49 is not listed so we look for df = 40 and one tail area = 0.05

t critical value = 1.684

Step 4) Decision rule:

Reject H0, if t test statistic value > t critical value , otherwise we fail to reject H0.

Since t test statistic value = 5.617 > t critical value = 1.684

we reject null hypothesis H0.

Step 5) Conclusion:

Since we have rejected H0, there is sufficient evidence to conclude that: the average weekly pay for all working women is significantly greater than that for women with a high school diploma.