Question

a researcher wants to find out if u.s. adults still support the death penalty at a proportion of 0.64 (as it was in 2003). this graph indicates the sampling distribution for the proportion of supporters in random samples of 25 adults. the standard deviation is approximately 0.10. what is the approximate test statistic for \\(\hat{p}=0.54\\)? a. -2 b. -1 c. 0 d. 1 e. 2

Explanation:

Step1: Recall test - statistic formula

The formula for the test - statistic $z$ in a proportion test is $z=\frac{\hat{p}-p}{\sigma_{\hat{p}}}$, where $\hat{p}$ is the sample proportion, $p$ is the hypothesized proportion, and $\sigma_{\hat{p}}$ is the standard deviation of the sampling distribution of the sample proportion.

Step2: Identify values

We are given that $\hat{p} = 0.54$, $p = 0.64$, and $\sigma_{\hat{p}}\approx0.10$.

Step3: Calculate the test - statistic

Substitute the values into the formula: $z=\frac{0.54 - 0.64}{0.10}=\frac{-0.1}{0.1}=- 1$.

Answer:

B. -1