Kia recently introduced a new electric vehicle, the EV6. To mark the introduction, Kia decided to produce 1,500 individually numbered First Edition EV6s. Reservations for First Edition EV6s opened several months in advance; within hours, all 1,500 were reserved. After the First Edition EV6s were produced, they were sold through Kia's dealer network. Kia allocated the First Edition EV6s to individual dealers, which then sold them to the individual reservation holders. Importantly, although Kia set the vehicles' "sticker" prices, the dealers determined the actual selling prices. After receiving numerous complaints, Kia decided to determine whether its dealers were marking up the First Edition EV6s' selling prices above the "sticker" prices. Kia surveyed the reservation holders and, of the sample of 286 reservation holders who responded, 131 said that they paid more than the vehicle's "sticker" price.

a. Determine the sample proportion, , that paid more than the "sticker" price. What is the expected number of the 1,500 First Edition reservation holders who paid more than the "sticker" price (round to the nearest whole number)?

b. In response to complaints, Kia wants to send a letter to First Edition EV6 reservation holders saying that most did not pay more than the "sticker" price. Develop the hypothesis test for the alternative hypothesis that less than 50% of First Edition EV6s were sold for more than the "sticker" price. Specifically, state the null hypothesis and compute the test statistic. Is this a one-tailed test to the left, a one-tailed test to the right, or a two-tailed test?

c. What is the p-value for the test statistic computed in [b]? Write the Excel function you used to determine this p-value, including the inputs that you entered in the Excel function (do not give cell references; write in the actual numbers).

d. Based on the results from [c], what is your conclusion at = .05 about the null hypothesis regarding the true proportion of First Edition EV6 reservation holders who paid more than "sticker" price.

e. Now compute a 90% confidence interval for the population proportion of reservation holders who paid more than the "sticker" price.

f. Is your hypothesis test conclusion from [d] consistent with the confidence interval in [e]? Why or why not?