An article in the San Jose Mercury News stated that students in the California State University

Question

An article in the San Jose Mercury News stated that students in the California state university system take 5 years, on average, to finish their undergraduate degrees. A freshman student believes that the mean time is less and conducts a survey of 68 students. The student obtains a sample mean of 4.5 with a sample standard deviation of 1.8. Is there sufficient evidence to support the student's claim at an a=0.05 significance level?Determine the test statistic. Find the p-value.



Answer 1

Ho: mu=5

H1: mu < 5

n=68, s=1.8, xbar= 4.5

alpha =.05 for 95% confidence level about z=1.645

one tailed test, n is large enough to use z instead of t distribution

z=(4.5-5)/s/sqrn = -.5/1.8/sqr68 = -.5/1.8)sqr68 = - .5/.9)sqr17

=about - 2.2906 > 1.645 standard deviations, reject Ho

use z tables or z calculator to find z calc and z crti

and p=about .011

reject Ho if zcalc>zcrit

or if p<alpha

.011<.05

on average it takes less than 5 years to graduate

(Sheldon Cooper could have done it in less than 1 year)