Suppose a 95 CI confidence interval for the proportion of ad

Suppose a 95% CI (confidence interval) for the proportion of adults that regularly attend a tae-kwan-do class at least once a week was found to be (0.2534, 0.3894).

a) For the null and alternative hypothesis: Ho: p = 0.40 versus Ha: p 0.40, what is your decision for this test of hypothesis?

b) Based on the CI, which of the following statements gives the best conclusion about the true value of the proportion of adults that regularly attend a tae-kwon-do class at least once a week?

i) I am 95% confident that the proportion of adults that regularly attend a tae-kwon-do class at least once a week is greater than 40%.

ii) I am 95% confident that the proportion of adults that regularly attend a tae-kwon-do class at least once a week is different than 40%.

iii) I am 95% confident that the proportion of adults that regularly attend a tae-kwon-do class at least once a week is less than 40%.

iv) I am 95% confident that the proportion of adults that regularly attend a tae-kwon-do class at least once a week equals 40%.

Solution

a)If the confidence interval contains the true value of the parameter the null hypothesis can’t be rejected. Since, here the interval does not contain the true value of the parameter=0.40, thus it may be concluded that the null hypothesis has been rejected.

b) Based on the CI (0.2534,0.3894)

iii) I am 95% confident that the proportion of adults that regularly attend a tae-kwon-do class at least once a week is less than 40%.