The mean sales price for new homes in Red County is $417,500. A sample of 65 home sales in the South showed a sample mean of $403,600. The population standard deviation is $51,500.

Formulate the null and alternative hypotheses that can be used to test the claim that the population mean for new homes in the South is lower than the County mean of $417,500. Use a 0.02 significance level.

What is the Rejection rule and is the p-value?

What is your conclusion?

Is the claim valid?