Question

Suppose that 600 students we selected at random from a student body and given a vaccine to prevent a certain type of flu. The campus reported cases of the flu so the students were exposed. A follow-up survey found that 562 of them did not get the flu.

a. Calculate the sample estimate of the proportion of the shot being successful.

b. Construct a 95% confidence interval around the sample estimate. This is a proportion and all the information you need for the standard deviation and standard error are presented above. For the confidence interval you will need the estimate, the z-value, the bound of error (BOE), and the lower and upper values of the confidence interval.

c. Suppose the proportion of the population that does not get the flu tends to be around 90%. Conduct a hypothesis test that the true value is not equal to .9. Note: this means the standard error will be based on the null value!

a. Include all the steps in the null hypothesis and include the p-value for your result.

b. Is there sufficient evidence from this sample to claim that the flu shot was effective? Effective means the rate of not getting the flu for the vaccinated students is higher. Use an alpha level of .05.

Answer 1

Solution:-) we have the following information:- Total number of students are 600. 562 of them did not get the flu.

a) The sample estimate of the shot being successful is :-

b) the standard error is given by:-

The 95 % C.I. is given by

c) The null and alternative hypothesis will be ;-

The standard error is given by:-

The z- statistic will be

From table ,the two-tailed P value equals 0.0028

As p-value< 0.05 (significance level). Therefore we reject the null hypothesis that not getting the flu for the vaccinated students is not equal to 0.9 .