Question

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 $\alpha =0.05$significance level of

$$\begin{gathered} H_0:\mu =115 \\ {H}_a:\mu >115 \end{gathered}$$

where $\mu =$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.

Short answer

The required answer is:

Yes, the conditions are fulfilled.

Step-by-step solution

Given information

Hypothesized population mean $\left({\mu }_0\right)=115$

Sample size $\left(n\right)=45$

Level of significance $\left(\alpha \right)=0.05$

The null and alternative hypotheses are as follows:

$$\begin{gathered} H_0:\mu =115 \\ {H}_a:\mu >115 \end{gathered}$$

The objective is to check whether the conditions required to perform the hypothesis test for the population mean are satisfied or not. 

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

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.