Q. 63 - The Practice of Statistics for AP

Question

Attitudes The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures students’ attitudes toward school and study habits. Scores range from $0 to 200$. 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 an SRS of $45$ of the over $1000$ students at her college who are at least $30$ years of age. Check the conditions for carrying out a significance test of the teacher’s suspicion.

Step-by-Step Solution

Answer

The teacher selected an SRS of $45$ students. $10\%: 45$ is less than $10\%$ of the population size of $1000$. Normal/Large Sample: $n=45\ge 30$

Step 1: Given information

Scores range from $0 to 200$. 

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 an SRS of$45$ of the over $1000$ students at her college who are at least $30$ years of age.

Step 2: Explanation

The teacher wants to perform a test at the α=0.05 significance level of

$$\begin{gathered} H_O:\mu =115 \\ Ha:\mu >115 \end{gathered}$$

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.

The teacher selected an SRS of $45$ students.

$10\%: 45$ is less than $10\%$ of the population size of $1000$.

Normal/Large Sample: $n=45>30$