To test the hypothesis that 55% of those families who plan to purchase a vacation residence in Florida want a condominium, the null hypothesis is π = 0.55 and the alternate is π ≠ .55. A random sample of 400 families who planned to buy a vacation residence revealed that 228 families want a condominium. What decision should be made regarding the null hypothesis using the 0.01 level of significance?
A) Do not reject it.
B) Reject it.
C) Cannot accept it or reject it based on the information given.
D) Purchase a condominium.

Question

Quizplus · Accepted Answer

The sample proportion of families who want a condominium is 228/400 = 0.57. The standard error of the proportion is sqrt(0.55*0.45/400) = 0.024. The z-score is (0.57 - 0.55) / 0.024 = 0.83. The p-value is P(|Z| > 0.83) = 2*P(Z > 0.83) = 2*0.2033 = 0.4066. Since the p-value is greater than the significance level of 0.01, we fail to reject the null hypothesis.

To Test the Hypothesis That 55% of Those Families Who