Provide an appropriate response.

The city management company claims that 75% of all low income housing is smaller than 1500 sq. ft. The tenants believe the proportion of housing this size is smaller than the claim, and hire an independent engineering firm to test a random sample size of 120 and found 79 houses were smaller than 1500 sq. ft. Should the city continue with its assumption of 75%? Test an appropriate hypothesis using α = 0.05 and state your conclusion. Be sure the appropriate assumptions and conditions are satisfied before you proceed.

a. z = 2.28; P-value = 0.9887. The change is statistically significant. A 98% confidence interval is (56.6%, 75.0%). This is clearly lower than 75%. The chance of observing 79 or less houses smaller than 1500 sq. ft. of 120 is 98.87% if the small housing is really 75%.

b. z = 2.32; P-value = 0.0102. The city should continue with its claim. There is a 1.02% chance of having 79 or less of 120 houses in a random sample be smaller than 1500sq. ft. if in fact 75% do.

c. z = -2.28; P-value = 0.9887. The city should continue with its claim. There is a 98.87% chance of having 79 or less of 120 houses in a random sample be smaller than 1500sq. ft. if in fact 75% do.

d. z = -2.32; P-value = 0.0102. The change is statistically significant. A 90% confidence interval is (58.7%, 73.0%). This is clearly lower than 75%. The chance of observing 79 or less houses smaller than 1500 sq. ft. of 120 is 1.02% if the small housing is really 75%.

e. z = -2.28; P-value = 0.0226. The change is statistically significant. A 95% confidence interval is (58.1%, 73.6%). This is clearly lower than 75%. The chance of observing 79 or less houses smaller than 1500 sq. ft. of 120 is 2.26% if the small housing is really 75%.