Question

House prices: Data from the National Association of Realtors indicates that the mean price of a home in Denver, Colorado, in 2012 was 260.7 thousand dollars. A random sample of 60 homes sold in 2013 had a mean price of 293 thousand dollars. Can you conclude that the mean price in 2013 is greater than the mean price in 2012? Assume the population standard deviation is o=155. Use the a = 0.10 level of significance and the critical value method. Part: 0/7 Part 1 of 7 (a) State the appropriate null and alternate hypotheses. Ho This hypothesis test is a (Choose one) test.

Answer 1

Solution:

Here, we have to use one sample z test for the population mean.

The null and alternative hypotheses are given as below:

H₀: µ = 260.7

H₁: µ > 260.7

This hypothesis test is a right-tailed (upper-tailed) test.

The test statistic formula is given as below:

Z = (x̄ - µ)/[σ/sqrt(n)]

From given data, we have

µ = 260.7

x̄ = 293

σ = 155

n = 60

α = 0.1

Critical value = 1.2816

(by using z-table or excel)

Z = (293 - 260.7)/[ 155/sqrt(60)]

Z = 1.6142

Test statistic = 1.6142

Test statistic > Critical value

So, we reject the null hypothesis

There is sufficient evidence to conclude that the mean price in 2013 is greater than the mean price in 2012.