Question

In 1970, 570 students among 1000 randomly selected college freshmen thought that capital punishment should be abolished. in 2005, 480 students among 1000 randomly selected college freshmen thought that capital punishment should be abolished. grades my media what is the two-sample z test statistic for evaluating the null hypothesis that the percentage of students who support capital punishment did not change from 1970 to 2005? round your answer to two decimal places.

Answer 1

The two-sample z-test statistic for evaluating the null hypothesis that the percentage of students who support capital punishment did not change from 1970 to 2005 is approximately 5.70.

Step-by-step explanation:

To calculate the two-sample z-test statistic for this data, we use the following steps:

1. First, identify the sample proportions. In 1970, with 570 out of 1000 students thinking that capital punishment should be abolished, the sample proportion is p1 = 570/1000 = 0.57. In 2005, the sample proportion is p2 = 480/1000 = 0.48.
2. Second, compute the pooled sample proportion. Since we are testing the null hypothesis that the two proportions are equal, we assume they are equal and compute a combined proportion from both samples. The pooled proportion (p) is (570+480)/(1000+1000) = 1050/2000 = 0.525.
3. Third, calculate the standard error (SE) of the sampling distribution of the difference between proportions. SE = sqrt[p * (1-p) * (1/n1 + 1/n2)] where n1 and n2 are the sample sizes (both 1000 in this case). SE = sqrt[0.525 * (1-0.525) * (1/1000 + 1/1000)] = sqrt[0.525 * 0.475 * 0.002] = sqrt[0.000249375] ≈ 0.0158.
4. Fourth, calculate the z-test statistic using the formula z = (p1 - p2) / SE. Thus, z = (0.57 - 0.48) / 0.0158 ≈ 5.70.

Therefore, the two-sample z-test statistic for evaluating the null hypothesis that the percentage of students who support capital punishment did not change from 1970 to 2005 is approximately 5.70, rounded to two decimal places.