In a recent survey conducted by Pew Research, it was found that 156 of 295 adult

Question

In a recent survey conducted by Pew Research, it was found that 156 of 295 adult Americans without a high school diploma were worried about having enough saved for retirement.

Does the sample evidence suggest that a majority of adult Americans without a high school diploma are worried about having enough saved for retirement?

a) What would it mean to make a Type II error for this test?

b) If the researcher decides to test this hypothesis at the 0.05 level of significance, determine the probability of making a Type II error if the true population proportion is 0.54. What is the power of the test?

Explanation / Answer

a) type II errorr would be accepting that minority or equal proportion  of adult Americans without a high school diploma are worried about having enough saved for retirement.

b)phat =156/295=0.5288 ; n=295

here std error od sample proportion =(phat(1-phat)/n))1/2 =0.029

for 0.05 level ' z=1.64485

hence critical value =sample proportion+z*std error =0.5766

std error of true mean =(p(1-p)/n)1/2 =0.029

hence type II error =P(P<0.5766)=P(Z<(0.5766-0.54)/0.029)=P(Z<1.262)=0.8965

hence power of test =1-P(type II error)=1-0.8965=0.1035

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

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