Chapter 9, Problem R9.2RE

To determine

To Explain: the appropriate tests to perform the setting and show the condition for carrying out the test are met.

Answer to Problem R9.2RE

1. t test for the mean for the one sample
2. z test for the proportion for one sample

Explanation of Solution

One sample z test is for a proportion p when interested in testing a claim about a proportion and one sample t test is for a mean when interested in testing a claim about a mean.

1. Claim about a mean and therefore using a one sample t test for the mean.

Conditions

Random: Satisfied, the reason is that the sample is simple random sample.

Independent: satisfied, the reason is that the sample of 48 female graduates is less than 10% of the population of all female graduates in the local high school.

Large sample: satisfied, the reason is that the sample size of 48 is bigger than 30 and therefore the sample is large.

Although all conditions are satisfied, it is suitable to perform a hypothesis test for the population mean.

2. Claim about the proportion and therefore using a one sample z test for the proportion $\begin{array}{c}p\text{=0}\text{.25}\\ n\text{ = 80}\end{array}$

   Conditions

   Random: Satisfied, the reason is that the sample is a random sample.

   Independent: Satisfied, the reason is that the sample of 80 students in the school is less than 10% of the population of all students in the school.

   Normal: satisfied, the reason is that

     $\begin{array}{c}np=80\left(0.25\right)=20\\ n\left(1-p\right)=80\left(1-0.25\right)\\ =60\end{array}$

   Both are at least 10

   Although, all the above conditions are satisfied, it is suitable to find the confidence interval for the population proportion p.