Question

A realtor in Florida claims that more than 75% of retired couples prefer apartment living to single-unit housing. A random sample of 100 couples shows that 81 prefer apartment living. Test the claim of the realtor at the 5% level of significance. (Hint: The realtor's claim, that more than 75% prefer apartment living, corresponds to the alternative hypothesis. The null will state that 75% prefer apartment living)

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.75

H_a : p > 0.75

= x / n = 81 / 100 = 0.81

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.81 - 0.75 / [(0.75 * 0.25) / 100]

= 1.386

P-value = 0.0829

= 0.05

P-value >

Fail to reject the null hypothesis .

There is sufficient evidence to suggest that the realtor in Florida claims that more than 75% of retired couples prefer apartment living to single-unit housing