The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures students' attitudes toward school and study habits. Scores range from 0 to 200, with higher scores indicating more positive attitudes and better study habits. The mean score for U.S. college students is about 115. A teacher suspects that older students have better attitudes toward school. She gives the SSHA to a simple random sample (SRS) of 45 of the more than 1000 students at her college who are at least 30 years of age.

State appropriate hypotheses for performing a significance test.

A. [tex]H_0: \bar{x}=115 ; H_a: \bar{x} > 115[/tex]

B. [tex]H_0: \mu > 115 ; H_a: \mu=115[/tex]

C. [tex]H_0: \mu=115 ; H_a: \mu > 115[/tex]

D. [tex]H_0: \bar{x} > 115 ; H_a: \bar{x}=115[/tex]

We begin by noting that the mean score for U.S. college students is given as [tex]$115$[/tex]. The teacher suspects that older students have more positive attitudes toward school, which means that for these students the mean score might be higher than [tex]$115$[/tex]. Therefore, when setting up our hypotheses for the significance test, we have:

1. The null hypothesis ([tex]$H_0$[/tex]) represents the claim that there is no difference; that is, the mean score for older students is still [tex]$115$[/tex]. This is written as:
[tex]$$H_0: \mu = 115.$$[/tex]

2. The alternative hypothesis ([tex]$H_a$[/tex]) reflects the teacher's suspicion that older students have a higher score. This is written as:
[tex]$$H_a: \mu > 115.$$[/tex]

These hypotheses set up a one-tailed test (specifically, a right-tailed test) because we are testing whether the mean score is greater than [tex]$115$[/tex].

Thus, the correct set of hypotheses is:

[tex]$$H_0: \mu = 115 \quad \text{and} \quad H_a: \mu > 115.$$[/tex]