Question

A rental agent claims that the mean monthly rent for apartments on the east side of town is less than $750. A random sample of 18 monthly rents for apartments on the east side has a mean of $737, with a standard deviation of $23.

If we assume that the monthly rents for apartments on the east side are normally distributed, is there enough evidence to conclude, at the .05 level of significance, that the mean is less than $750?

Answer 1

Its statistically significant, that Mean monthly apartment rent in town east < $ 750

Explanation:

Null Hypothesis [H0] : Mean monthly apartment rent in town east = 750

Alternate Hypothesis [H1]: Mean monthly apartment rent in town east < 750

t = (x' - u) / (s / √n)

x' = sample mean = 737

u = population assumed mean = 750

s = standard deviation = 23

n = no. of units in sample

t = (737 - 750) / (23 / √18) = -13 / 5.4212

= -2.39

t tabulated critical value : for one sided 0.05 significance level, at 17 degrees of freedom = -1.740

t calculated value, -2.39 < t tabulated critical value, - 1.740

We reject the null hypothesis, & state that its statistically significant, that Mean monthly apartment rent in town east < 750