Question

Suppose the mean price for used cars is $10,198. A manager of a Kansas City used car dealership reviewed a sample of 50 recent used car sales at the dealership in an attempt to determine whether the population mean price for used cars at this particular dealership differed from the national mean. The prices for the sample of 50 cars are shown in the file named usedcars. What statistical test should the manager use to compare the mean price for used cars at this dealership with the national mean?

1) Z-test
2) T-test
3) Chi-square test
4) ANOVA

Answer 1

To compare the mean price for used cars at the Kansas City dealership with the national population mean, the manager should use a t-test, which is suitable in the absence of known population standard deviation and when working with a sample size like 50.

Step-by-step explanation:

The appropriate statistical test to compare the mean price for used cars at this Kansas City dealership with the national population mean would be a t-test. A t-test is used when comparing sample means to a known population mean, especially when the population standard deviation is unknown and the sample size is small (typically less than 30). However, since the sample size in this scenario is larger (50 cars), the t-distribution would still be appropriate, given that the sample standard deviation will be used as an estimate because the true population standard deviation is not provided.

The steps the manager would follow to conduct the t-test include stating the null hypothesis that there is no difference between the dealership's mean price and the national mean price, selecting an appropriate significance level, calculating the t-statistic using the sample data, and comparing the t-statistic to the critical value from the t-distribution table to determine whether to reject or fail to reject the null hypothesis.