Question

You are investigating whether apartments in the Philadelphia area are larger than the national average. The mean size of all apartments in the U.S. was 941 square feet in 2018. For a randomly selected sample of 23 renters in Philadelphia, you ask them how big their apartment is, measured in square feet. You find that their mean apartment size is 835 square feet. Assume that the population standard deviation is 173 square feet. Does your sample data provide evidence significant at the 10% level that Philadelphia apartments are smaller than the national average? State your conclusion in a complete sentence. (5 points)

Answer 1

Ans:

$H_0:\mu =941$

$H_a:\mu <941$

sample mean=835

population standard deviation=173

n=23

Test statistic:

z=(835-941)/(173/sqrt(23))

z=-2.94

p-value=P(z<-2.94)=0.0016

As,p-value<0.1,we reject the null hypothesis.There is sufficient evidence to conclude that Philadelphia apartments are smaller than the national average.