You randomly choose 16 unfurnished one-bedroom apartments from a large number of advertisements in your local newspaper. You calculate that their mean monthly rent is $613 and their standard deviation is $96. 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.
Fill in the blanks:
The t statistic is ______ (give your answer to 3 decimal places) with df = _____ (Give your answer as a whole number) and P-value of ______ (Give your answer to 4 decimal places)
I know the first two are
1.753
15
but i've no idea how to calculate p-value
t = 2.625
df = n-1 = 15
P-value = 0.0096
To calculate the p-value, you will need to perform a t-test. The p-value represents the probability of observing a sample mean as extreme or more extreme than the one calculated, assuming the null hypothesis is true.
In this case, the null hypothesis (H0) is that the mean rent of all advertised one-bedroom apartments is not greater than $550. The alternative hypothesis (Ha) is that the mean rent is greater than $550.
To calculate the p-value, you will need to use the t-distribution. Follow these steps:
1. Determine the test statistic (t statistic) using the formula:
t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))
In this case:
Sample mean (x̄) = $613
Hypothesized mean (μ) = $550
Sample standard deviation (s) = $96
Sample size (n) = 16
Plugging the values into the formula:
t = ($613 - $550) / ($96 / sqrt(16))
t = $63 / ($96 / 4)
t = $63 / $24
t ≈ 2.625
2. Determine the degrees of freedom (df) which can be calculated as (sample size - 1). In this case, df = 16 - 1 = 15.
3. Calculate the p-value using a t-table or statistical software:
For a one-tailed test with df = 15 and t = 2.625, the p-value is approximately 0.0095 or 0.0094 (when rounded to 4 decimal places).
Therefore, the completed information is as follows:
The t statistic is approximately 2.625 with df = 15 and a p-value of approximately 0.0095 (or 0.0094 when rounded to 4 decimal places).