Question

1. Inference from two independent samples. The data in the previous question (?̅ = 217,900, ? = 91,200, ? = 25) was from 2013. The real estate agent believes that home prices have increased in the five years since then. In order to assess whether or not this is true, she gathers data on a new random sample of 40 existing single-family home sales from her neighborhood in 2018. The average sale price from her 2018 sample is ?̅ = 252,900 and the sample standard deviation is ? = 105,700.

a. What are the agent’s null and alternative hypotheses?

b. Calculate the z-score and p-value for part (a)’s hypotheses using Table C from the appendix. Do not use Excel. In order to prove that you didn’t use Excel, you must show the steps of your work, including a brief (one or two sentences will suffice) explanation of how exactly you used Table C. For the degrees of freedom, you should use the conservative approach that we discussed in class. (As we also discussed in class, you will only be able to place an upper and lower bound on the p-value if you use Table C for hypothesis testing.)

c. Is the mean price in 2018 greater than the mean price in 2013 at the 10% level of significance? 5%? 1%?

d.Construct a 90% confidence interval for the difference between the average sale price in 2018 and the average sale price in 2013. Use Table C from the appendix. Do not use Excel. In order to prove that you didn’t use Excel, you must show the steps of your work, including a brief (one or two sentences will suffice) explanation of how exactly you used Table C.

Answer 1

1- PRICE IN 2018

2- price in 2013

p-value is between 0.05 and 0.10

hence

we reject the null hypothesis at 0.10 level ,

we fail to reject the null hypothesis at 0.05 and 0.01 level

90 % confidence interval of difference

The 90% confidence interval is    −7741.763<μ1​−μ2​<77741.763.