Question

Suppose your hypothesis is that the average price of a two bedroom home in Little Rock is $150,000. You sample 17 homes and find an average price of $145000 with a standard deviation of 7,500. Set up the null hypothesis, and the alternate hypothesis (you can write this out in words). Show the test statistic, the critical statistic, and the results of your hypothesis test. (A) Test the hypothesis at the 10% significance level (B) Test the hypothesis at 5% significance level (C) Test the hypothesis at 1% significance level.

Answer 1

Solution:

The null and alternative hypotheses are:

H0: The average price of a two-bedroom home in Little Rock is $150,000.

Ha: The average price of a two-bedroom home in Little Rock is not $150,000.

Symbolically, the null and alternative hypotheses are:

The test statistic is:

(A) Test the hypothesis at the 10% significance level

The t-critical values at the 0.10 significance level for df=n-1=17-1=16 are:

Conclusion: Since the test statistic falls in the rejection region, we, therefore, reject the null hypothesis and conclude that the average price of a two-bedroom home in Little Rock is not $150,000 at the 0.10 significance level.

(B) Test the hypothesis at 5% significance level

The t-critical values at the 0.05 significance level for df=n-1=17-1=16 are:

Conclusion: Since the test statistic falls in the rejection region, we, therefore, reject the null hypothesis and conclude that the average price of a two-bedroom home in Little Rock is not $150,000 at the 0.05 significance level.

(C) Test the hypothesis at 1% significance level.

The t-critical values at the 0.01 significance level for df=n-1=17-1=16 are:

Conclusion: Since the test statistic does not fall in the rejection region, we, therefore, fail to reject the null hypothesis and conclude that the average price of a two-bedroom home in Little Rock is $150,000 at the 0.01 significance level.