Part 1:
Use the heights of the statistics students at FTCC
I. Point Estimate
A. When estimating a population mean, are you more likely correct when you use a point estimate or an interval estimate? Explain your reasoning.
B.Which statistic is the best unbiased estimator for the population mean? Explain.
C.For the same sample statistics, which level of confidence would produce the widest confidence interval? Explain your reasoning.
II.Margin of Error and Confidence Interval
A. State the mean and standard deviation of the heights data set. Round to the nearest tenth.
B.Find the following margin of errors using your sample statistics above with the following level of confidence. Round to the nearest tenth.
1.C = .90
2.C = .95
3.C = .99
C. Construct the confidence interval for each of the confidence levels in part B above. Round to the nearest tenth.
D.Height of adults are known to be normally distributed with a mean of 69 inches(taken fromhttp://www.fas.harvard.edu) Based on our data from students here at FTCC, do you think that this information is correct. Why or why not? Explain.
III.Sample Size
A. What would be a reasonable margin of error for your data set if you had to decide independently? Explain your reasoning. If you were doing a study on the heights of adults, how wide should be the margin of error. (Example: within 1 in, within ½ in…)
B. Determine the minimum sample size required to be 95% confident given your standard deviation and the margin of error that you decided on in part A as reasonable for your data set. Use s as an approximation ofs.
C.What happens to your minimum sample size if you increase or decrease your margin of error for your data set? Explain.
Part 2:
I have done some research online about the heights and have set up hypothesis for you to perform. You are to use the same sample data that you used above to test the hypothesis below that is about your data. Set up your hypothesis and then perform each step below labeling the values and explaining what you are doing.
Height:
Your instructor at FTCC claims that the students are short at this college. I did some research online and found that the average height of an adult human is 69 inches. At a significance level of 0.05, test the instructors claim that the mean height of students at this college is less than the average height of an adults in the US. (taken fromhttp://www.fas.harvard.edu/~loebinfo/loebinfo/Proportions/humanfigure.html )
IV.Hypothesis
A. State your claim.
B. State your Null Hypotheses.
C.State the Alternative Hypotheses.
D.Describe the two types of error possible in a hypothesis test decision.
I.
II.
III.
IV.
V.Finding P-Values and Rejection Regions
A. Identify the type of test you are going to conduct.
B.What is the level of significance that you are going to use to test your Hypotheses?
C.Calculate the test statistic and its corresponding standardized test statistics. Round to 3 decimal places.
D.Find the Critical values and rejection region(s)
E.Find the P-value. Round to 5 decimal places.
VI.Interpret the decisions.
A. What is your decision concerning your Null Hypotheses?
B.Write a statement to interpret the decision in the context of the original claim.
Part 3
:
In Module 3, we looked at the hours of sleep that FTCC students get each night. I found online that the average hours of sleep that an adult gets is 6.8 hours. Does this seem likely based on our sample of students? You should show all work supporting this claim and write a paragraph explaining your decision.
· You can use Intervals or Hypothesis testing to prove or disprove this claim. You will choose the confidence level or significance level.
·Show all steps in the chosen process.
oIf you do a hypothesis test, include the claim, hypothesis, significance level, so on…
oIf you do an interval, give confidence level, margin of error, so on…
·Explain your reasoning in detail. Why do you think that the average is 6.8 hours or not 6.8 hours? Back up your opinion using the statistical information.
·You should write one paragraph explaining the results of your statistical process.
Part 4
:
In Module 3, we looked at the GPAs of FTCC students. I found online source that claims the average GPA of college students in the US is 3.11. Does this seem likely based on our sample of students? You should show all work supporting this claim and write a paragraph explaining your decision.
· You can use Intervals or Hypothesis testing to prove or disprove this claim. You will choose the confidence level or significance level.
·Show all steps in the chosen process.
oIf you do a hypothesis test, include the claim, hypothesis, significance level, so on…
oIf you do an interval, give confidence level, margin of error, so on…
·Explain your reasoning in detail. Why do you think that the average GPA is 3.11 or is not 3.11? Back up your opinion using the statistical information.
·You should write one paragraph explaining the results of your statistical process.