Chapter 9: Q. 65. (page 606)

Attitudes The Survey of Study Habits and Attitudes (SSHA) is a
psychological test with scores that range from $0$ to $200 .$ . The mean score for U.S. college students is $115$ . A teacher suspects that older students have better attitudes toward school. She gives the SSHA to an SRS of $45$ students from the more than $1000$ students at her college who are at least $30$ years of age. The teacher wants to perform a test at the $α = 0.05$ significance level of
$H_{0} : μ = 115 H_{a} : μ > 115$
where $μ =$ the mean SSHA score in the population of students at her college who are at least $30$ years old. Check if the conditions for performing the test are met.

Expert verified

The required answer is:

Yes, the conditions are fulfilled.

Step by step solution

Hypothesized population mean $(μ_{0}) = 115$

Sample size $(n) = 45$

Level of significance $(α) = 0.05$

The null and alternative hypotheses are as follows:

$H_{0} : μ = 115 H_{a} : μ > 115$

The following conditions must be met before conducting a hypothesis test on $μ$ :

Simple random samples must be drawn from the population.

The sample size should be large, $n > 30$ and the population should be normally distributed.

Requirement check:

The $45$ -person sample was chosen using a simple random sampling technique.

The sample size exceeds $30$ people.

Therefore, both the required conditions are met.

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