Question

a new policy for certain social groups is known to be effective in 31% of the groups administered.

(a) Out of 25 selected groups who have social problems, what is the mean (expected value) and standard deviation of groups for whom the policy will be effective?

(b) Out of 25 groups selected, what is the probability that the number of groups for whom the treatment will be effective is at least 5?

(c) Suppose that the policy was successful for 18 out of 100 groups selected. Does this provide evidence that the true proportion of cases that the policy is effective in is different from 31%, as stated previously in the problem? Use a significance level of 0.05, and the P-value to give your decision.

Claim:

Ho:

Ha:

Test Statistic:

P-value:

Result of the hypothesis test (Decision):

Interpretation of the result in the complete English sentences, using the context of the problems:

(D) Construct a 95% confidence interval for the population p, and explain how this leads to the same decision you arrived at in part (c)

Answer 1