Cushman and Wakefield accounting that the average annual rent for office space in Tampa was $17.63 per square foot. A real estate agent selected a random sample of 15 rental properties (offices) and found that mean rent was $18.72 per square foot and s= $3.64. At a= 0.05, test the claim that agents the mean rent is greater than $17.63.
Z = (mean1 - mean2)/standard error (SE) of difference between means
SEdiff = √(SEmean1^2 + SEmean2^2)
SEm = SD/√n
If only one SD is provided, you can use just that to determine SEdiff.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.
To test the claim that the mean rent is greater than $17.63 per square foot, we can perform a one-sample t-test. Here are the steps to calculate the t-test:
Step 1: State the hypotheses:
- Null Hypothesis (H0): The mean rent is equal to $17.63 per square foot.
- Alternative Hypothesis (Ha): The mean rent is greater than $17.63 per square foot.
Step 2: Set the significance level:
In this case, the significance level (α) is given as 0.05, which means we will reject the null hypothesis if the p-value is less than 0.05.
Step 3: Calculate the test statistic:
The formula to calculate the t-test statistic is:
t = (x̄ - μ) / (s / √n),
where
x̄ is the sample mean ($18.72),
μ is the population mean ($17.63),
s is the sample standard deviation ($3.64),
n is the sample size (15).
Plugging in the values, we get:
t = ($18.72 - $17.63) / ($3.64 / √15)
Step 4: Find the critical value:
Since the alternative hypothesis is one-tailed (greater than), we need to find the critical value for a one-tailed t-test with a degrees of freedom (df) equal to n - 1. In this case, df = 15 - 1 = 14.
Using a t-table or a statistical calculator, find the critical value with a significance level of 0.05 and 14 degrees of freedom.
Step 5: Calculate the p-value:
Using the t-value from Step 3 and the degrees of freedom, calculate the p-value associated with the t-distribution.
Step 6: Make a decision:
If the p-value is less than the significance level (0.05), we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
Keep in mind that these calculations can be done using a statistical software or a scientific calculator with t-test capabilities.