Question

You are conducting a study to see if the proportion of women over 40 who regularly have mammograms is significantly less than 0.24. You use a significance level of ?=0.05.

      H0:p=0.24
      H1:p<0.24

You obtain a sample of size n=536 in which there are 123 successes.

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) ?? or greater than ??

This p-value leads to a decision to...

reject the null, accept the null, or 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 women over 40 who regularly have mammograms is less than 0.24.

There is not sufficient evidence to warrant rejection of the claim that the proportion of women over 40 who regularly have mammograms is less than 0.24.

The sample data support the claim that the proportion of women over 40 who regularly have mammograms is less than 0.24.

There is not sufficient sample evidence to support the claim that the proportion of women over 40 who regularly have mammograms is less than 0.24.

Answer 1

The statistical software output for this problem is:

One sample proportion summary hypothesis test:
p : Proportion of successes
H₀ : p = 0.24
H_A : p < 0.24

Hypothesis test results:

Proportion	Count	Total	Sample Prop.	Std. Err.	Z-Stat	P-value
p	123	536	0.22947761	0.018447182	-0.57040627	0.2842

Hence,

p - Value = 0.2842

The p - value is greater than ?

fail to reject the null

There is not sufficient sample evidence to support the claim that the proportion of women over 40 who regularly have mammograms is less than 0.24. Option D is correct.