University administrators are trying to decide where to build a new parking garage on campus. The state legislature has budgeted just enough money for one parking structure on campus. The administrators have determined that the parking garage will be built either by the college of engineering or by the college of business. To help make the final decision, the university has randomly and independently asked students from each of the two colleges to estimate how long they usually take to find a parking spot on campus (in minutes). Suppose that the sample sizes selected by the university for the two samples were both $\mathrm { n } _ { \mathrm { e } } = \mathrm { n } _ { \mathrm { b } } = 15$ . What critical value should be used by the university in the calculations for the 95% confidence interval for ?e - ?b? Assume that the university used the pooled estimate of the population variances in the calculation of the confidence interval.
A) z = 1.645
B) z = 1.96
C) t = 2.042
D) t = 2.048
E) t = 1.701

Question

Quizplus · Accepted Answer

Since the sample sizes are small (n < 30) and the population standard deviations are unknown, the t-distribution should be used. With degrees of freedom calculated as $ n_e + n_b - 2 = 28 $, the critical value for a 95% confidence interval is approximately 2.048.

University Administrators Are Trying to Decide Where to Build a New