(Use the following information for the next four questions.)
A large clothing manufacturer plans to introduce a new line of sports clothes for women if preliminary market research shows that at least 50% of the population are favorably impressed by the new line. Five hundred women were surveyed; 265 of the women were favorably impressed. The research manager wants to test the hypothesis at the .05 significance level. The z-value associated with this significance level is 1.645.
-The calculated z-statistic for testing the hypothesis is:
A) 1.339
B) -1.339
C) 0.977
D) -0.977
E) more information is needed

Question

Quizplus · Accepted Answer

The calculated z-statistic is found using the formula for a proportion test: $z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$, where $\hat{p}$ is the sample proportion, $p_0$ is the null hypothesis proportion (in this case, 0.5), and $n$ is the sample size. Given $\hat{p} = \frac{265}{500} = 0.53$, $p_0 = 0.5$, and $n = 500$, the calculation yields a z-value of approximately 1.339, indicating the observed proportion is 1.339 standard deviations above the hypothesized proportion.

(Use the Following Information for the Next Four Questions