Question

Question 6 2.5 pts A statistics professor believes that his students are above average intelligence. To test this, he collects a random sample of 50 of his students' IQ scores and finds a sample mean of 110. Knowing that the mean population IQ is 100 with a standard deviation of 15, he calculates a z of x-bar test statistic of 4.72. Based on this information, what statistical decision should this professor come to? O Fail to reject the null, because 4.72 > 1.645 Reject the null, because 4.72 > 1.96 O Reject the null, because 4.72 > 1.645 Fail to reject the null, because 4.72 > 1.96

Answer 1

Here , we want to test the claim that , $H_1:\mu>100$

The null and alternative hypothesis is , $H_0:\mu=100;H_1:\mu>100$

The test is one-tailed test.

Now , to assume that the significance level is

g= 0,05

The critical value is , $Z_{\alpha}=Z_{0.05}=1.645$

Since , the test statistic is , Z-stat=4.72

The decision rule is , Reject the null hypothesis if Z-stat>1.645 , otherwise fail to reject the null hypothesis.

Decision : Here , reject the null hypothesis because 4.72>1.645