Please show your work

1. Explain why it is important to calculate a confidence interval when we do not have data from the entire population. Why can't we just use a sample mean?

1. Explain the meaning of the term "95% confidence" in the following scenario without using the word "confident" or "confidence" (or synonyms like certain, sure...) in the part you must add.

Scenario:

You are measuring the length of fish in a pond and want to know the mean length of the population of fish. You must begin your explanation with "Assume I have data from 100 samples of fish taken from the pond and I have calculated the 95% confidence interval for each of these samples. I know that the true population mean will be found in...

3. For a fixed level of confidence, what happens to a confidence interval forwhen we decrease the sample size?

4. Suppose that for a sample size of n=144, we find that the sample mean is 48. Assuming that the standard deviation = 7, calculate the confidence intervals for the population meanwith the following confidence levels.

a. 90%

b. 92%

c. 95%

d. 97%

e. 99%

5. Compare the shape of the t curve to the shape of the z curve. What are their similarities and differences?

6. 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 97 and you know the population standard deviation. Will you be using z or t?