Question

A fashion magazine provides a yearly subscription service. According to historical data, about 72% of the customers renew their subscriptions each year. The manager of the magazine office believes the percentage would be higher if they change their service to be a monthly subscription. After 12 months, the manager randomly selected 500 customers and found 387 of them renewed the subscription. She conducts a hypothesis test where H0:p=0.72, and Ha:p>0.72 at the α=.05 level. She finds the p-value is 0.0036.

Select one or more:

a. 0.0036 is the probability of having 387 or fewer customers renew their subscription in a sample of 500 customers given that the true proportion of renewing subscription is 0.72.

b. 0.0036 is the probability of having exactly 387 customers renew their subscription in a sample of 500 customers given that the true proportion of those who renew their subscription is 0.72.

c. 0.0036 is the probability of having 387 or more customers renew their subscription in a sample of 500 customers given that the true proportion of those who renew their subscription is 0.72.

d. Because the p-value 0.0036 is not higher than 0.05, it is not statistically significant at that level, so we fail to reject the null hypothesis.

e. Because the p-value 0.0036 is less than 0.05, it is statistically significant at that level, and so we should reject the null hypothesis in favor of the alternative hypothesis.

f. 0.0036 is the probability that the true proportion of customers who renew their subscription is 0.72.

Answer 1

H0 : p = 0.72

Ha :p > 0.72

sample proportion = 387 / 500 = 0.774

under null hypothesis Ho: p = 0.72

p value = Pr[p > 0.774] = 0.0036

p - value means probability of having 387 or more customers renew their subscription in a sample of 500 customers given that the true proportion of those who renew their subscription is 0.72.

Hence option c is correct.

also if p value is less than level of significance we reject null hypothesis.

in our case p value = 0.0036 < 0.05 = level of significance , Hence we reject null hypothesis.

Hence option e is correct.

Because the p-value 0.0036 is less than 0.05, it is statistically significant at that level, and so we should reject the null hypothesis in favor of the alternative hypothesis.

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