Question

Note: For this problem, your answer should be rounded to two decimal places.

In a particular municipality, it is believed that 25 percent of homes are not properly insulated. In order to test ?0:?=.25 vs. ??:?≠.25 (where ? is the population proportion of homes that are not properly insulated) a random sample of 300 homes was selected. In the sample, it was found that 90 homes were not properly insulated.

If the null hypothesis is true, then the z-score for the sample proportion is:

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H0 : p = 0.25

Ha : p 0.25

= x / n = 90 / 300 = 0.30

P0 = 0.25

1 - P0 = 1 - 0.25 = 0.75

Test statistic = z =

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

= 0.30 - 0.25/ [(0.25 * 0.75) / 300]

Test statistic = z = 2.00