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 = 0.86, and Ha: p <0.86 at the α = 0.5 level. She finds the p-value is 0.0323.
Select one or more:
A. 0.0323 is the probability of having 289 or more customers renew teir subscription in a sample of 350 customers given that the true proportion of renewing subscription is 0.86.
B. 0.0323 is the probability of having exacly 289 customers renew their subscrption in a sample of 350 customers given that the true proportion of those who renew their subscription is 0.86.
C. 0.0323 is the probability of having 289 or fewer customers renew their subscription in a sample of 350 customers given that the true proportion of thos who renew their subscription is 0.86.
D. Because the p-value 0.0323 is ont 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 0.0323 is less than 0.05, it is not statistically significant at that level, and so we should reject the null hypothesis in favor of the alternative hypothesis.

The correct statements are (A) and (E).

Step-by-step explanation:

The hypothesis to be tested is defined as follows:

H₀: The proportion of customers who renew their subscriptions each year is 72%, i.e. p = 0.72.

Hₐ: The proportion of customers who renew their subscriptions each year is more than 72%, i.e. p > 0.72.

The significance level of the test is, α = 0.05.

The p-value of the test statistic is, p-value = 0.0323.

The p-value is well defined as per the probability, [under the null hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was truly observed.

The p-value of 0.0323, implies that 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 0.86 is 0.0323.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.

p-value = 0.0323 < α = 0.05.

Thus, the null hypothesis will be rejected at 5% level of significance.

The correct statements are (A) and (E).

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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