Question

You are conducting a study to see if the proportion of women over 40 who regularly have mammograms is significantly less than 0.84. You use a significance level of α=0.05α=0.05.

      H0:p=0.84H0:p=0.84
      H1:p<0.84H1:p<0.84

You obtain a sample of size n=161n=161 in which there are 122 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) αα
• greater than αα

This p-value 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 women over 40 who regularly have mammograms is less than 0.84.
• 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 0.84.
• The sample data support the claim that the proportion of women over 40 who regularly have mammograms is less than 0.84.
• There is not sufficient sample evidence to support the claim that the proportion of women over 40 who regularly have mammograms is less than 0.84.

Answer 1

We have to test, H0: p = 0.84 against H1: p < 0.84

The test-statistic is given by, Z = , where, = 122/161 = 0.7578, p = 0.84, n = 161

Thus, Z = - 2.8450

Under H0, Z ~ N(0,1).

The p-value is = P(Z < - 2.8450) = (-2.8450) = 0.0022

[(.) is the cdf of N(0,1)]

The p-value < level of significance = 0.05, so we reject the null hypothesis H0.

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 0.84.