A random sample of eight students participated in a psychological test of depth perception. Two markers, one labeled A and the other B, were arranged at a fixed distance apart at the far end of the laboratory. One by one the students were asked to judge the distance between the two markers at the other end of the room. The sample data (in feet) were as follows:

2.2, 2.3, 2.7, 2.4, 1.9, 2.4, 2.5, 2.6

At the alpha = 0.05 level of significance, test if the mean distance is more than 2 feet

(a)   State the null and alternative hypothesis.

(b)  Give the p-value

(c)   Give a conclusion for the hypothesis test.

(d)  Find a 95% Confidence Interval.

(e)  Write a conclusion for the confidence interval