Question

House prices: Data from the National Association of Realtors indicate that the mean price of a home in Denver, Colorado, in December 2016 was 366.5 thousand dollars. A random sample of 50 homes sold in 2017 had a mean price of 396.3 thousand dollars. a. Assume the population standard deviation is σ = 150. Can you conclude that the mean price in 2017 differs from the mean price in December 2016? Use the α = 0.05 level of significance. b. Following is a boxplot of the data. Explain why it is not reasonable to assume that the population is approximately normally distributed. c. Explain why the assumptions for the hypothesis test are satisfied even though the population is not normal.

Answer 1

(a)

H0: Null Hypothesis: = 366.5

HA: Alternative Hypothesis: 366.5

SE = /

= 150/ = 21.2132

Test statistic is:
Z = (396.3 - 366.5)/21.2132 = 1.4048

= 0.05

From Table, critical values of Z = 1.96.

Since the calculated value of Z = 1.4048 is less than critical value of Z = 1.96, the difference is not significant. Fail to reject null hypothesis.

Conclusion:

The data do not support the claim that the population mean is different from 366.5,the mean price in December 2016.

(c) Since the sample size = n = 50 > 30, Large sample and also the population standard deviation is provided, Central Limit Theorem applies and the sampling distribution of sample mean is Normal distribution irrespective of the shape of the population.Thus the assumptions for the hypothesis test are satisfied even though the population is not normal.