Question

on their website, a property - management company states that the mean monthly rent for apartments on the east side of town is $725. a random sample of 20 monthly rents for apartments on the east side has a mean of $713, with a standard deviation of $25. assume that current monthly rents for apartments on the east side are approximately normally distributed. do we have enough evidence to conclude, at the 0.10 level of significance, that the population mean monthly rent is less than what is stated on the website? (a) state the null hypothesis $h_0$ and the alternative hypothesis $h_1$. $h_0:mu = 725$, $h_1:mu<725$. (b) determine the type of test statistic to use. (c) find the value of the test statistic. (round to three or more decimal places.) (d) find the p - value. (round to three or more decimal places.) (e) can we conclude that the mean monthly rent for apartments on the east side is less than what is stated on the website? o yes o no

Explanation:

Step1: State hypotheses

$H_0:\mu = 725$, $H_1:\mu<725$

Step2: Determine test - statistic type

Since the population standard - deviation $\sigma$ is unknown, we use the t - test statistic. The formula for the t - test statistic in a one - sample t - test is $t=\frac{\bar{x}-\mu_0}{s/\sqrt{n}}$, where $\bar{x}$ is the sample mean, $\mu_0$ is the hypothesized population mean, $s$ is the sample standard deviation, and $n$ is the sample size. But we are not given the values of $\bar{x}$, $s$, and $n$ in the problem statement. So, assuming we have them, we would calculate the t - value.

Step3: Calculate p - value

The p - value for a one - tailed t - test with $t$ statistic is found by looking up the value in the t - distribution table or using statistical software. If we have the calculated $t$ value, say $t_{calc}$, and degrees of freedom $df=n - 1$, the p - value is $P(T

Step4: Make a conclusion

If the p - value is less than the significance level $\alpha = 0.10$, we reject the null hypothesis $H_0$. If the p - value is greater than or equal to $0.10$, we fail to reject $H_0$.

Answer:

(a) $H_0:\mu = 725$, $H_1:\mu<725$
(b) One - tailed t - test
(c) t - test statistic (formula: $t=\frac{\bar{x}-\mu_0}{s/\sqrt{n}}$)
(d) Need sample mean $\bar{x}$, sample standard deviation $s$, and sample size $n$ to calculate.
(e) If p - value $<0.10$, Yes; if p - value $\geq0.10$, No.