Testing a Claim - Essay
Testing a Claim
It is possible to test a claim using a confidence interval. The logic is very simple and straightforward. Assume we use StatCrunch to create a 95% confidence interval for the number of Facebook friends for Kaplan University MM207 students and find that the interval is between 75 friends and to 125 friends. Now, one of your classmates claims that the average number of Facebook friends is 150. Does this claim make sense in light of your confidence interval? No it does not. If a claim is not within a specified confidence interval then we should not accept the claim as reasonable. If a claim is within the confidence interval then we should accept the claim as reasonable. Now, we know that we could be wrong, based on the confidence level selected for the interval. In our example, we would be 95% confident that the average is between 75 and 125 friends so we would not accept our classmates claim that the average is 150 as reasonable. But, we could be wrong 5% of the time so we do not state we proved it wrong, only that our data suggest that the claim is not reasonable.
Here is another example.
A psychologist claims that the average score on the Short Form Intelligence Test (SFIT) for Kaplan University students is 115. While you agree that Kaplan students are generally brighter than the average person, you believe this might not be correct. You take a sample of 30 Kaplan students and give them the SFIT. Using the data from this administration you determine the sample mean to be 109 and the sample standard deviation to be 11.8.
Using StatCrunch, "Z Statistics--One Sample-- with summary" you get the following output:
90% confidence interval results: μ : population mean
Standard deviation = 11.8 Mean | n | Sample Mean | Std. Err. | L. Limit | U. Limit | μ | 30 | 109 | 2.1543753 | 105.45637 | 112.54363 |
From the output we are 90% confident that the true population mean SFIT score for all Kaplan students is between 105.46 and
It is possible to test a claim using a confidence interval. The logic is very simple and straightforward. Assume we use StatCrunch to create a 95% confidence interval for the number of Facebook friends for Kaplan University MM207 students and find that the interval is between 75 friends and to 125 friends. Now, one of your classmates claims that the average number of Facebook friends is 150. Does this claim make sense in light of your confidence interval? No it does not. If a claim is not within a specified confidence interval then we should not accept the claim as reasonable. If a claim is within the confidence interval then we should accept the claim as reasonable. Now, we know that we could be wrong, based on the confidence level selected for the interval. In our example, we would be 95% confident that the average is between 75 and 125 friends so we would not accept our classmates claim that the average is 150 as reasonable. But, we could be wrong 5% of the time so we do not state we proved it wrong, only that our data suggest that the claim is not reasonable.
Here is another example.
A psychologist claims that the average score on the Short Form Intelligence Test (SFIT) for Kaplan University students is 115. While you agree that Kaplan students are generally brighter than the average person, you believe this might not be correct. You take a sample of 30 Kaplan students and give them the SFIT. Using the data from this administration you determine the sample mean to be 109 and the sample standard deviation to be 11.8.
Using StatCrunch, "Z Statistics--One Sample-- with summary" you get the following output:
90% confidence interval results: μ : population mean
Standard deviation = 11.8 Mean | n | Sample Mean | Std. Err. | L. Limit | U. Limit | μ | 30 | 109 | 2.1543753 | 105.45637 | 112.54363 |
From the output we are 90% confident that the true population mean SFIT score for all Kaplan students is between 105.46 and