Test at the 0.01 level the statement that 55% of those families who plan to purchase a vacation residence in Florida want a condominium. The null hypothesis is $\pi$ = 0.55 and the alternate is $\pi$ $\neq$.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?
A) Do not reject it
B) Reject it
C) Cannot accept nor reject it based on the information given
D) Purchase a condominium.

Question

Quizplus · Accepted Answer

The sample proportion is 228/400 = 0.57. The standard error is $\sqrt{(0.55 \times 0.45) / 400}$. The z-score is $(0.57 - 0.55) / \text{standard error}$. At the 0.01 level, the critical z-values are approximately ±2.576. The calculated z-score does not exceed these critical values, so we do not reject the null hypothesis.

Test at the 0 π\piπ = 055 and the Alternate Is π\piπ

Test at the 0 $\pi$ = 055 and the Alternate Is $\pi$