Week 5 – Confidence Intervals
38634. A company surveyed its employees to determine what the new daily meal allotment dollar amount should be. Of the 100 employees, 62 responded. Pat’s supervisor asked what the recommended dollar amount should be. Pat could take the mean of the 62 responses or calculate a confidence interval about the mean using those 62 responses. Which action of the two (don’t go outside these choices) would give the supervisor a better idea of what the true mean is, and why?
2. You are catching fish in a pond and measuring the length of fish. You want to know the mean length of the population of fish, but you also know you can never be sure you have caught and measured all the fish, so you decide to use confidence intervals. You catch fish 10 at a time, measure their lengths, and create 95% confidence intervals each time. Assume you have data from 100 samples of fish taken from the pond and have calculated the 95% confidence interval for each of these samples.
a. Why will you have different confidence intervals for each of your trials?
b. How many of those 100 confidence intervals will contain the true population mean? Why?
3. You take one of your samples of fish and calculate the 95% confidence interval for the mean length of the fish, and you compare it to the 99% confidence interval for the same sample. Did the range of the interval increase or decrease, and why?
4. Your samples usually contained 10 fish. You have been calculating the 95% confidence interval for the mean length of the fish for each sample. Let’s say that your next sample contained 50 fish. If you calculated the 95% confidence interval for the sample of 50 fish, would the range of its 95% confidence interval from this sample of 50 be larger or smaller than the range of the 95% confidence interval when the sample size was 10 fish? Why?
5. Suppose that for a sample size of n=50, we find that the sample mean is 12 inches. Assuming that the standard deviation = 1.6 inches, calculate the confidence intervals for the population mean µ with the following confidence levels.
a. 90%
b. 92%
c. 95%
d. 97%
e. 99%
6. Compare the shape of the t curve to the shape of the z curve. What are their similarities and differences?
7. Locate a flowchart online which helps you determine when to use t and when to use z in your calculations. The flow chart should include knowledge of population standard deviation and sample size. Embed it in this assignment. Cite your source. Explain how to use the flowchart given this scenario:
You have a sample size of 19 and you do not know the population standard deviation. Will you be using z or t?
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