Question

The U.S. Census Bureau reported that the mean area of U.S. homes built in 2012 was 2505 square feet. A simple random sample of 19 homes built in 2013 had a mean area of 2738 square feet with a standard deviation of 280 feet. Can you conclude that the mean area of homes built in 2013 is greater than the mean area of homes built in 2012? It has been confirmed that home sizes follow a normal distribution. Use a 10% significance level. Round to the fourth H 0 : H A : Test Statistic: P-value: Did something significant happen? Select the Decision Rule: There enough evidence to conclude

Answer 1

Solution :

= 2505

= 2738

s = 280

n = 19

This is the right tailed test .

The null and alternative hypothesis is

H0 :   = 2505

Ha : > 2505

Test statistic = t

= ( - ) / s / n

= (2738 - 2505) /280 / 19

= 3.627

p(t >3.627 ) = 1-P (t< 3.627 ) =0.0010

P-value = 0.0010

= 0.10  

0.0010< 0.10

Reject the null hypothesis .

There is enough evidence to suggest that