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.

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.

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.

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 $p$