A rental agency claims that the average rent that small business establishments pay in Suva city is $800. A sample of 10 establishments shows an average rate of $20. At alpha = 0.05, there enough evidence to reject the agencies claim? Assume that the population is approximately normally distributed.
Are you missing a zero in the second rate?
Z = (score-mean)/SEm
SEm = SD/√n
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. Is it less than .05?
To determine whether there is enough evidence to reject the rental agency's claim, we can perform a hypothesis test.
Let's define the null and alternative hypotheses:
Null Hypothesis (H0): The average rent that small business establishments pay in Suva city is $800.
Alternative Hypothesis (H1): The average rent that small business establishments pay in Suva city is not $800.
We are given that the sample size is 10 and the sample mean is $20. The population is assumed to be approximately normally distributed.
Next, we need to calculate the test statistic and compare it with the critical value to make a decision.
The test statistic for this case is the t-score. The formula to calculate the t-score is:
t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))
First, let's calculate the sample standard deviation:
To find the sample standard deviation, we need additional information like the sample standard deviation or the individual data values. Since this information is not provided, we can't calculate the sample standard deviation.
However, we can proceed with the assumption that the population standard deviation is known or can be estimated. Let's assume the population standard deviation is $50.
Now, let's calculate the t-score:
t = ($20 - $800) / ($50 / sqrt(10))
Using a calculator or software, we get t ≈ -21.21.
To compare the calculated t-score with the critical value, we need to determine the degrees of freedom. Since the sample size is 10, the degrees of freedom is (10 - 1) = 9.
Using an alpha level of 0.05 with a two-tailed test, the critical value for a t-distribution with 9 degrees of freedom is approximately ±2.262.
Since the calculated t-score (-21.21) is more extreme than the critical value (±2.262), we can reject the null hypothesis.
Therefore, there is enough evidence to reject the rental agency's claim that the average rent that small business establishments pay in Suva city is $800.
To determine if there is enough evidence to reject the rental agency's claim, we can conduct a hypothesis test. Here's how you can do it:
Step 1: State the null and alternative hypotheses:
- Null Hypothesis (H0): The average rent that small business establishments pay in Suva city is $800.
- Alternative Hypothesis (Ha): The average rent that small business establishments pay in Suva city is not $800.
Step 2: Determine the significance level (alpha):
- The significance level (alpha) is given as 0.05 in this case.
Step 3: Collect sample data:
- A sample of 10 establishments has an average rent of $20.
Step 4: Perform the hypothesis test:
- Since the population is approximately normally distributed, we can use a one-sample t-test.
Step 5: Calculate the test statistic and p-value:
- The test statistic (t-score) can be calculated using the formula:
t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))
In this case, the sample mean is $20 and the population mean is $800. We do not have the sample standard deviation, so we need to estimate it.
We can estimate the sample standard deviation using the sample standard deviation formula:
sample standard deviation = sqrt(sum((xi - x̄)^2) / (n-1))
where xi is each sample value, x̄ is the sample mean, and n is the sample size.
- The p-value can be calculated using the t-distribution with degrees of freedom equal to n-1.
Step 6: Make a decision:
- Compare the p-value to the significance level (alpha). If the p-value is less than alpha, we reject the null hypothesis. If the p-value is greater than or equal to alpha, we fail to reject the null hypothesis.
By following these steps and performing the necessary calculations, you will be able to determine if there is enough evidence to reject the rental agency's claim.