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Dr. Woz and Dr. Yaz want to test whether violent video games have an effect on aggressive thinking in high school youth. In order to measure aggressive thinking, the researchers are going to use a test developed at GTA University. The test has shown that scores greater than 70 on the test indicate that the subject is more likely to agree with statements that endorse aggressive behavior. The researchers select a random sample of n = 200 youth from an after-school program for the study. Each of the students spends an hour playing a first-person shooter-type video game and then takes the test. The mean and standard deviation for the sample is mean = 72.5 and s = 20. The researchers would like to know if the sample mean of 72.5 is statistically significantly different from 70 using a two-tailed test with α < .05 and critical values of t of ±1.96. a. The null hypothesis for this test would be that the test average =? Ho: µ = 70. b. What is the estimated standard error for this test? The estimated standard error for this test is s/√n = 20/√200. c. Calculate the value of the t statistic: The t statistic is calculated as (sample mean - hypothesized mean) / (estimated standard error) = (72.5 - 70) / (20/√200). d. Is this test "one-tailed" or "two-tailed"? This test is two-tailed. e. Does the t statistic fall in the "critical region"? To determine if the t statistic falls in the critical region, we compare it to the critical values of t. If the t statistic is greater than the positive critical value or less than the negative critical value, it falls in the critical region. f. Do you accept or reject the null hypothesis? To determine whether to accept or reject the null hypothesis, we compare the t statistic to the critical values of t. If the t statistic falls in the critical region, we reject the null hypothesis. Otherwise, we accept the null hypothesis. e. Why are the researchers described using a t test rather than a Z test? The researchers are using a t test rather than a Z test because the population standard deviation is unknown, and the sample size is relatively small (n = 200). Therefore, a t test is more appropriate for this scenario.

Dr. Woz and Dr. Yaz want to test whether violent video games have an effect on aggressive thinking in high school youth. In order to measure aggressive thinking, the researchers are going to use a test developed at GTA University. The test has shown that scores greater than 70 on the test indicate that the subject is more likely to agree with statements that endorse aggressive behavior. The researchers select a random sample of n = 200 youth from an after-school program for the study. Each of the students spends an hour playing a first-person shooter-type video game and then takes the test. The mean and standard deviation for the sample is mean = 72.5 and s = 20. The researchers would like to know if the sample mean of 72.5 is statistically significantly different from 70 using a two-tailed test with α < .05 and critical values of t of ±1.96.

a. The null hypothesis for this test would be that the test average =?
Ho: µ = 70.

b. What is the estimated standard error for this test?
The estimated standard error for this test is s/√n = 20/√200.

c. Calculate the value of the t statistic:
The t statistic is calculated as (sample mean - hypothesized mean) / (estimated standard error) = (72.5 - 70) / (20/√200).

d. Is this test "one-tailed" or "two-tailed"?
This test is two-tailed.

e. Does the t statistic fall in the "critical region"?
To determine if the t statistic falls in the critical region, we compare it to the critical values of t. If the t statistic is greater than the positive critical value or less than the negative critical value, it falls in the critical region.

f. Do you accept or reject the null hypothesis?
To determine whether to accept or reject the null hypothesis, we compare the t statistic to the critical values of t. If the t statistic falls in the critical region, we reject the null hypothesis. Otherwise, we accept the null hypothesis.

e. Why are the researchers described using a t test rather than a Z test?
The researchers are using a t test rather than a Z test because the population standard deviation is unknown, and the sample size is relatively small (n = 200). Therefore, a t test is more appropriate for this scenario.

Added by Curtis C.

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