Question

You randomly choose 15 unfurnished one-bedroom apartments from a large number of advertisements in your local newspaper. You calculate that their mean monthly rent is $570 and their standard deviation is $105. Does this SRS give good reason to believe that the mean rent of all advertised one-bedroom apartments is greater than $550? State the hypotheses, find the t-statistic and its p-value, and state your conclusion.

Answer 1

If you can calculate t-statistic, surely you can make a start on this problem.

Answer 2

Under the normal distribution about 2.5% of values are greater than 2 standard deviations above the mean.

Answer 3

Second point, sample mean is 570 question is asked, do you think the true mean is > 550.

Answer 4

So the so-called null hypothesis, that this is not true, is that the true mean is not greater than 550

Answer 5

We are thinking about a one-tailed hypothesis test. The null hypothesis might be the population mean is $550 and the alternative hypothesis is that the population mean is greater than $550.
\[\large t=\frac{\bar{x}-\mu}{\frac{\sigma_\bar{x}}{\sqrt{n}}}\]

Answer 6

Very nice @Valpey

Answer 7

so i found to that the P-value is 0.2364. So does that mean this SRS does not give sufficient evidence against the null hypothesis? Like how do you know if it's sufficient evidence if you don't have alpha? That's where i'm confused.

Answer 8

@telliott99, @Valpey

Answer 9

i believe that if the p-value you determine lies outside of the 95% (2sds from the mean) that it qualifies for "unusual"

Answer 10

\[t>2z \cup\ t<2z:\ unusual\]