Question

Miss Gillmore claims that the percentage of restaurants that opened in Stars Hollow in the early 1980's and are still in business today is higher than 60%. We took a random sample of 43 restaurants that opened in Stars Hollow in the early 1980's, and 27 were still in business today. Using the data, perform a hypothesis test to test Miss Gillmore's claim using significance level=0.10.

Answer 1

Solution :

This is the righttailed test .

The null and alternative hypothesis is

H0 : p = 0.60

Ha : p 0.60

n =43

x =27

= x / n = 27 / 43 = 0.63

P0 = 0.60

1 - P0 = 1 - 0.60 = 0.40

Test statistic = z

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

=0.63 -0.60 / [(0.60*0.40) / 43]

= 0.37

Test statistic = z = 0.37

P(z > 0.37 ) = 1 - P(z < 0.37 ) = 1 - 0.6443

P-value = 0.3557

= 0.10

P-value >

0.3557 > 0.10

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that