Question

A report states the average rent for office space in a urban area is $17.75 per square foot. A real estate agent claims this average is incorrect. The agent selected a sample of 26 rental properties and found their mean to be $19.25 per square foot, with a sample standard deviation of $3.55 per square foot. Test the claim at alpha = 0.10. Use the P-value method to evaluate/compare with the given alpha (0.10

Answer 1

Solution :

Given that,

Population mean = = 17.75

Sample mean = = 19.25

Sample standard deviation = s = 3.55

Sample size = n = 26

Level of significance = = 0.10

This is a two tailed test.

The null and alternative hypothesis is,

Ho: 17.75

Ha: 17.75

The test statistics,

t = ( - )/ (s/)

= ( 19.25 - 17.75 ) / ( 3.55/26)

= 2.155

df = n - 1 = 25

P- Value = 0.041   

The p-value is p = 0.041 < 0.10, it is concluded that the null hypothesis is rejected.

Conclusion :

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean μ is different than 17.75, at the 0.10 significance level.