Jillian was told that the average IQ of a freshman at her college was no greater than 118. To test this, she gave an IQ test to 44 freshmen. She found an average of 120.09 with [tex]s = 8.08[/tex]. Which of the following correctly describes the test and hypotheses she should use?

A. A t-test with [tex]H_0: \mu = 118[/tex], [tex]H_a: \mu \neq 118[/tex]
B. A t-test with [tex]H_0: \mu \leq 118[/tex], [tex]H_a: \mu > 118[/tex]
C. A z-test with [tex]H_0: \mu \leq 118[/tex], [tex]H_a: \mu > 118[/tex]
D. A z-test with [tex]H_0: \mu = 118[/tex], [tex]H_a: \mu \neq 118[/tex]
E. Cannot satisfy normality; do not test

Suppose that she performs the test correctly but that a Type I error occurred. What happened?

A. She found that the average IQ was greater than 118 when it actually wasn’t.
B. She found that the average IQ was not greater than 118 when it actually was.
C. She found that the average IQ was not greater than 118 when it actually wasn’t.
D. She found that the average IQ was greater than 118 when it actually was.

Jillian should perform a t-test with the null hypothesis stating that the average IQ is less than or equal to 118, correct option is B. The alternative hypothesis that the average IQ is more than 118.Correct option is A.

Jillian should use a t-test for assessing her hypothesis. The appropriate hypotheses would be H0:μ≤118, stating that the average IQ is less than or equal to 118, and Ha:μ>118, stating that the average IQ is more than 118. These hypotheses align with her initial statement about the average IQ.

A Type I error is a statistical term indicating that a test has mistakenly rejected a true null hypothesis (H0). If Jillian made a Type I error in this scenario, it means she found that the average IQ was greater than 118 when it actually wasn’t (option A). This error, also known as a 'false positive', is where you reject the null hypothesis when it is, in fact, true.

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