Question

HW #42 #5

You are conducting a study to see if the proportion of men over 50 who regularly have their prostate examined is significantly less than 0.32. You use a significance level of α=0.002α=0.002.

      H0:p=0.32H0:p=0.32
      HA:p<0.32HA:p<0.32

You obtain a sample of size n=372n=372 in which there are 96 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) αα
• greater than αα

This test statistic leads to a decision to...

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

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 less than 0.32.
• 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 less than 0.32.
• The sample data support the claim that the proportion of men over 50 who regularly have their prostate examined is less than 0.32.
• There is not sufficient sample evidence to support the claim that the proportion of men over 50 who regularly have their prostate examined is less than 0.32.

Answer 1

from the results in r,

Test statistic is ,

Chi Squared=6.176

Degrees of freedom=1

p value = 0.0061

p value < 0.05( level of significance)

Therefore we reject the null hypothesis at 5% level of significance.

So we can conclude that,

Therefore there is sufficient evidence to support the claim that the proportion of men over 50 who regularly have their prostrate examined is less than 0.32.