Question

Checking conditions Refer to Exercise R9.1. Identify the appropriate test to

perform in each setting and show that the conditions for carrying out the test are met.

Short answer

a. $t-$test for the mean for the one sample

b. $z$test for the proportion for one sample

Step-by-step solution

Part (a) Step 1: Given information

When evaluating a claim about a proportion, use a one-sample $z$ test, and when testing a claim about a mean, use a one-sample $t-$test.

Part (a) Step2: Calculation

Claim about a mean and therefore use a one-sample $t-$test for the mean.

Conditions

Random: The reason for my satisfaction is that the sample is a simple random sample.

Independent: The reason for this is that the sample of $48$female graduates represents less than $10\%$of the total number of female graduates in the local high school.

Large sample: The reason for this is that the sample size of $48$is more than $30$and hence the sample size is enormous.

Even though all of the prerequisites are met, a hypothesis test for the population mean is appropriate.

Part (b) Step 1: Calculation

As a result of the claim concerning the proportion, a one-sample $z-$test for the proportion was used.

$$\begin{gathered} p=0.25 \\ n=80 \end{gathered}$$

Conditions

Random: The reason for my satisfaction is that the sample is a random sample.

Independent: The reason for this is that the sample of $80$pupils at the school represents less than $10\%$of the total student population.

Normal: satisfied, the reason is that

$$\begin{gathered} np=80(0.25) \\ =20n(1-p) \\ =80(1-0.25) \\ =60 \end{gathered}$$

Both are at least $10$

Despite the fact that all of the preceding conditions are met, it is appropriate to calculate the confidence interval for the population percentage $p$