Final answer:
To conduct a hypothesis test, we set the null and alternative hypotheses and perform a t-test using sample data. We compare the p-value to a significance level to make a conclusion.
Step-by-step explanation:
To conduct a hypothesis test to determine whether the number of weeks until a house sold in Greene County differed from the national average in 2017, we need to set up the null and alternative hypotheses. The null hypothesis, denoted as H0, states that the population mean is equal to the national average. The alternative hypothesis, denoted as Ha, states that the population mean is different from the national average.
H0: µ = 3 (population mean is equal to the national average)
Ha: µ ≠ 3 (population mean is different from the national average)
Using the sample mean of 3.6 weeks, sample standard deviation of 2 weeks, and a sample size of 40, we can perform a t-test to calculate the test statistic and the p-value. By comparing the p-value to a significance level (e.g., 0.05), we can determine whether to reject or fail to reject the null hypothesis. If the p-value is less than the significance level, we reject the null hypothesis and conclude that the number of weeks until a house sold in Greene County differs from the national average.