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).
So i figured out that the t-stat is 1.753 and the df=15. but i don't know how to calculate the p-value.
To calculate the p-value, first, we need to find the critical value in the t-distribution table for the given degrees of freedom (df). In this case, the degrees of freedom are n - 1, where n is the sample size (16).
From the information given, the t-statistic is 1.753, and the degrees of freedom (df) are 15. Using these values, we can determine the p-value using the t-distribution table or statistical software.
To find the p-value in this case, we need to calculate the probability of observing a t-value as extreme as 1.753 given a t-distribution with 15 degrees of freedom. This probability corresponds to the area under the t-distribution curve to the right of the t-value.
Using statistical software or a t-distribution table, we find that the p-value for a t-value of 1.753 with 15 degrees of freedom is approximately 0.0984 (rounded to 4 decimal places).
Therefore, the p-value is approximately 0.0984.
To calculate the p-value, you need to use a t-distribution table or a t-distribution calculator. Here are the steps to calculate it:
1. State the null (H0) and alternative (Ha) hypotheses:
- Null hypothesis (H0): The mean rent of all advertised one-bedroom apartments is not greater than $550.
- Alternative hypothesis (Ha): The mean rent of all advertised one-bedroom apartments is greater than $550.
2. Calculate the 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 (μ0) = $550
- Sample standard deviation (s) = $96
- Sample size (n) = 16
t = ($613 - $550) / ($96 / √16)
= $63 / ($96 / 4)
= $63 / $24
= 2.625 (rounded to 3 decimal places)
3. Calculate the degrees of freedom (df):
The degrees of freedom for a t-test with a sample size of n = 16 is equal to (n - 1), which in this case is 15.
4. Use the t-distribution table or calculator to find the p-value associated with the t-statistic and df.
Since the alternative hypothesis is that the mean rent is greater than $550, you need to find the area under the right tail of the t-distribution.
Using a t-distribution table or calculator, the p-value for a t-statistic of 2.625 with 15 degrees of freedom is approximately 0.0094 (rounded to 4 decimal places).
Therefore, the completed information is as follows:
The t statistic is 2.625 (rounded to 3 decimal places), with df = 15 (whole number) and a p-value of 0.0094 (rounded to 4 decimal places).
Ho:µ= 550
Ha:µ> 550
t = (613-550)/(96/sqrt(16)
t = 2.625
p-value
Right-tailed
tcdf(2.625, 10, 15) = 0.0096