Question

A rental agent claims that the mean monthly rent,

μ

, for apartments on the east side of town is less than

$700

. A random sample of

14

monthly rents for apartments on the east side has a mean of

$694

, with a standard deviation of

$21

. If we assume that the monthly rents for apartments on the east side are normally distributed, is there enough evidence to conclude, at the

0.05

level of significance, that

μ

is less than

$700

?

Perform a one-tailed test. Then fill in the table below.

Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)

The null hypothesis: H0: The alternative hypothesis: H1: The type of test statistic: (Choose one)ZtChi squareF The value of the test statistic: (Round to at least three decimal places.) The p-value: (Round to at least three decimal places.) Using the 0.05 level of significance, can we conclude that the mean monthly rent for apartments on the east side is less than $700 ? Yes No

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 700
Alternative Hypothesis, Ha: μ < 700

This is t test

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (694 - 700)/(21/sqrt(14))
t = -1.069

P-value Approach
P-value = 0.152

As P-value >= 0.05, fail to reject null hypothesis.

We cannot conclude that the mean monthly rent for apartments on the east side is less than

$700