Question

A large university provides housing for 10 percent of its graduate students to live on campus. The university’s housing office thinks that the proportion of graduate students looking for housing on campus may be more than 0.10. The housing office decides to survey a random sample of graduate students, and 62 of 481 say that they are looking for housing on campus. At a=.05, is there evidence to support the housing office’s suspicion?

Answer 1

solution

This is the right tailed test .

The null and alternative hypothesis is

H0 : p =0.10

Ha : p >0.10

= x / n = 62/481=0.1289

P0 = 0.10

1 - P0 = 1-0.10=0.90

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

=0.1289-0.10 / [(0.10*0.9) /481 ]

Z= 2.11

P(z >2.11 ) = 1 - P(z < 2.11) = 1-0.9826=0.0174

P-value = 0.0174

= 0.05

P-value <

Reject the null hypothesis .

There is sufficient evidence to suggest that