Question

the wechsler adult intelligence scale (iq test) is constructed so that full scale iq scores follow a normal distribution, with a mean of 100, and a standard deviation of 15. the mayor of smart town believes the countys residents are smarter than the national average and wants to use it (the intelligence of the residents) as a marketing tool to bring industries to the area.
a researcher is hired to conduct a study to determine whether smart countys residents have, on average, higher full scale iqs than the population. a random sample of 100 people from smart county were given the iq test and were found to have an average full scale iq of 105.
which hypothesis test should be used to determine whether the mean full scale iq score of the smart county residents is higher than the national average?
a. ○ z - test for the population mean
b. ○ t - test for the population mean
c. ○ z - test for the population proportion
d. ○ t - test for the population proportion

Explanation:

Step1: Check the parameter of interest

The parameter of interest is the population mean (Full - Scale IQ score), so we can rule out options C and D (which are about population proportion).

Step2: Check the conditions for z - test and t - test

We know the population standard deviation ($\sigma = 15$). For a hypothesis test about the population mean, when the population standard deviation $\sigma$ is known, we use the z - test. The sample size $n=100$ (a large sample size, but even for normal populations with known $\sigma$, z - test is appropriate). The t - test is used when the population standard deviation is unknown and we estimate it using the sample standard deviation.

Answer:

A. z - test for the population mean