Question

Dr. Woz and Dr. Yaz want to test whether violent video games have an effect on aggressive thinking. In order to test aggressive thinking, Woz and Yaz 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. Dr. Woz and Dr. Yaz select a random sample of n = 100 children from a local primary school 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 M = 73 and s = 20. Woz and Yaz would like to know if the sample mean of 73 is statistically significantly different from 70 using a two-tailed test with α < .05 and critical values of t of ±1.98.

a. What is the null hypothesis for this test? H_o: µ =  

b. What is the estimated standard error for this test?  

c. Calculate the value of the t statistic:

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

e. Does the t statistic fall in the "critical region"?

f. Do you accept or reject the null hypothesis?  

Answer 1

Given that, sample size ( n ) = 100

sample mean ( M ) = 73 and sample standard deviation ( s ) = 20

critical value is, t^* = +/- 1.98

a) The null hypothesis for this test is,

H_o: µ = 70

the alternative hypothesis is,

b) The estimated standard error for this test is,

The estimated standard error for this test is 2

c) Test statistic is,

The value of the t statistic is 1.5

d) This is two-tailed test.

e) Critical region : t < -1.98 or t > 1.98

Here, t = 1.5 < 1.98

Therefore, the t statistic does not fall in the critical region

f) Since, t statistic is not fall in the critical region we should accept the null hypothesis.