In volleyball, a libero is a defensive specialist who can substitute for any back-row player but cannot attack or block the ball when it is above the net. Because of this restriction, liberos are often some of the shortest players on a team. Suppose that Jasmine wants to play volleyball in college but is worried she is too short to be seriously considered. She read online that the average libero on a college team is 67 inches tall, but she suspects that this is too low. Jasmine selects a random sample of 15 liberos on college volleyball teams. Their heights, in inches, are listed below. Assume that the height of all female liberos on college volleyball teams is normally distributed.

69,70,66,67,69,68,68,64,69,67,68,69,68,67,65

Jasmine decides to use a right‑tailed one‑sample t‑test to determine whether the average height of liberos on college volleyball teams is greater than 67 in.

Have the requirements for a one‑sample t‑test been met? If they have not been met, leave the remaining questions blank.

Choose the appropriate null and alternative hypotheses for this test.

Calculate the value of the one-sample t‑statistic. Give your answer precise to three decimal places.

Use a t‑distribution table such as this one to find a range of possible p‑values for this test.

Complete the conclusion of this test. Use a significance level of α=0.05 Jasmine should_____ her null hypothesis. There is_________ evidence that the mean height of liberos on college volleyball teams is______ 67in.