Question

You are conducting a study to see if the proportion of men over 50 who regularly have their prostate examined is significantly different from 0.17. You use a significance level of α=0.02.

      H0:p=0.17
      H1:p≠0.17

You obtain a sample of size n=428 in which there are 56 successes.

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

The p-value is...

• less than (or equal to) α

• greater than α

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the proportion of men over 50 who regularly have their prostate examined is different from 0.17.
• There is not sufficient evidence to warrant rejection of the claim that the proportion of men over 50 who regularly have their prostate examined is different from 0.17.
• The sample data support the claim that the proportion of men over 50 who regularly have their prostate examined is different from 0.17.
• There is not sufficient sample evidence to support the claim that the proportion of men over 50 who regularly have their prostate examined is different from 0.17.

Answer 1

n = 428, x = 56      

p̄ = x/n = 0.1308      

α =    0.02      

Null and Alternative hypothesis:          
Ho : p = 0.17 ; H1 : p ≠ 0.17      

Test statistic:          
z =(p̄ -p)/(√(p*(1-p)/n)) = -2.157      

p-value :          
p-value = 2*(1-NORM.S.DIST(ABS(-2.157), 1)) = 0.0310

The p-value is greater than α.

This test statistic leads to a decision to.

fail to reject the null

Final conclusion:

There is sufficient evidence to warrant rejection of the claim that the proportion of men over 50 who regularly have their prostate examined is different from 0.17.