You then survey 100 people and you discover that their average income is $45,000

Question

You then survey 100 people and you discover that their average income is $45,000 with a standard deviation of $2,500.  Your hypothesis is that the income is $50,000 or greater. The conventional wisdom is that some people is not as affluent as other. Set up the null hypothesis, and the alternate hypothesis (you can write this out in words) and test the hypothesis. Show the test statistic, the critical statistic, and the results of your hypothesis test. (A) Test this hypothesis at 10% level of significance. (B) Test this hypothesis at the 5% level of significance. (C) Test this hypothesis at the 1% level of significance.

Explanation / Answer

here null hypothesis: mean income<=50000

alternate hypothesis: mean income>50000

here degree oif freedom =n-1=99

here critrical value at 10% level =1.2902

critrical value at 5% level =1.6604

critrical value at 1% level =2.3646

here std error =std deviation/(n)1/2 =250

hence test stat t=(x-MEAN)/std error =(45000-50000)/250=-20

for above p value =1 ; as test is right tailed

hence we can not reject null hypothesis; that income is below 50000 on any level as p vlaue is greater then any significance level and test stat is less then critical value for right tailed test.

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.