Question

A women’s health center is conducting a study to see if the proportion of women over 40 who regularly have mammograms is significantly more than 0.55. They are using a significance level of α = 0.05to evaluate their results. The findings from a sample of size 205 are that 130 women over 40 regularly have mammograms. (Show all steps please)

a) State the null and alternative hypothesis (H0 and Ha). H0: Ha:

b)What is the test statistic for this sample (use at least 3 decimal places)?

c) What is the p-value for this sample? (use Statcrunch)

d) Evaluate the strength of the evidence and state the conclusion (in the context of this question).

Answer 1

a) As we are testing here whether the proportion is more than 0.55, therefore this is a one tailed test for which the null and the alternative hypothesis here are given as:

b) The test statistic here is computed as:

Therefore 2.422 is the required test statistic value here.

c) As this is a one tailed test, the p-value here is obtained as:
p = P(Z > 2.422) = 0.0077

Therefore 0.0077 is the required p-value here.

d) As the p-value here is 0.0077 < 0.05 which is the level of significance, therefore the test is significant and we can reject the null hypothesis here. Therefore we have sufficient evidence here that the population proportion is more than 0.55.