Question

According to data from the National Association of Home Builders, the average size of new homes in the United States was 2320 square feet in a recent year. Suppose a random sample of 400 new homes was taken and the mean of this sample showed the average size of the homes was 2365 square feet. With a population standard deviation of 312 square feet can you accept the claim that home data from the National Association of Home Builders is correct? Use an alpha of 0.05 to solve.

Answer 1

Solution :

= 2320

=2365

=312

n = 400

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :    = 2320

H_a :     2320

Test statistic = z

= ( - ) / / n

= (2365-2320) / 312 / 400

= 2.88

Test statistic = z = 2.88

P(z >2.88 ) = 1 - P(z < 2.88 ) = 1 -0.9980

P-value =0.0020

= 0.05  

P-value <

0.0020 < 0.05

Reject the null hypothesis .

There is sufficient evidence to suggest that