Everything in the assignment should to be done by excel and using appropriate EXCEL formulae. The assignment is also attached as pdf, thank you
Question 1: The Transactional Records Access Clearinghouse at Syracuse University reported data showing the odds of an Internal Revenue Service (IRS) audit. The following table shows the average adjusted gross income reported and the percent of the returns that were audited for 20 selected IRS districts.
Table of values in the attachment.
(a) Enter the data in EXCEL, use EXCEL to find all required components to develop the estimated regression equation that could be used to predict the percent audited given the average adjusted gross income reported. Label your answers.
(b) At the 0.05 level of significance, determine whether the adjusted gross income and the percent audited are linearly related.
(c) Did the estimated regression equation provide a good fit? Explain.
(d) Use the estimated regression equation developed in part (a) to calculate a 95% confidence interval for the expected percent audited for districts with an average adjusted gross income of $35,000.
Question 2: Executives at the Walt Disney Company are interested in estimating the mean spending per capita for people who visit Disney World in Orlando, Florida. Since they do not know the population standard deviation, they plan to use the t-distribution to conduct the test. However, they realize that the tdistribution requires that the population be normally distributed. Six hundred customers were randomly surveyed, and the amount spent during their stay at Disney World was recorded. These data are in the file called Disney.xls. Before using these sample data to estimate the population mean, the managers wish to test whether the population is normally distributed.
(a) State the appropriate null and alternative hypotheses.
(b) Organize the data into six classes and form the grouped frequency distribution.
(c) Using the sample mean and sample standard deviation, calculate the expected frequencies, assuming that the null hypothesis is true.
(d) Conduct the test statistic and compare it to the appropriate critical value for a significance level equal to 0.05. What conclusion should be reached? Discuss.
Question 3: Symptoms of diabetes include increased thirst and frequent urination (especially at night), unexplained increase in appetite, unexplained weight loss, fatigue, blurred vision, and tingling or numbness in the hands or feet. If your fasting blood glucose level is between 5.5 mmol/L (100 mg/dL) and 6.9 mmol/L (126 mg/dL), you are considered to have pre-diabetes (impaired fasting glucose), and you have an increased chance of developing diabetes. Other conditions that can cause high blood glucose levels include severe stress, heart attack, stroke, Cushing’s syndrome, medicines such as corticosteroids, or excess production of growth hormone (acromegaly). The Canadian Diabetes Association (CDA) criteria for diagnosing diabetes are met when any of the following results have been repeated on at least two different days:
– A fasting blood glucose level is 7.0 mmol/L (126 mg/dL) or higher.
– A 2-hour oral glucose tolerance test result is 11.1 mmol/L (200 mg/dL) or higher. For more information, see the medical test Oral Glucose Tolerance Test.
– Symptoms of diabetes are present and a random blood glucose test is 11.1 mmol/L (200 mg/dL) or higher.
Part I: At a diabetic clinic, a group of people considered to have pre-diabetes (impaired fasting glucose) were randomly selected. Then they were randomly assigned in two groups, namely treatment groups (subject to a strict diet plan) and placebo (normal diet), for a specified number of days. After the completion of the clinical trial, their blood glucose level readings provided the following statistics:
Placebo: n1 = 10, x1 = 6.5, s1 = 0.21
Treatment: n2 = 10, x2 = 5.4, s2 = 0.17 2
Assume the assumptions of normality are satisfied.
(a) Is it reasonable to assume equality of variances in this problem? Justify your answer.
(b) Do the data provide sufficient evidence at the 5% significance level that the strict diet plan lowers the blood glucose level? What is the appropriate conclusion?
(c) What is the p-value for this test?
(d) Using p-value approach and = 0.10, what conclusion can be drawn about the difference in average blood glucose level readings between treatment and placebo groups? (e) Estimate with 95% confidence the difference in mean blood glucose levels between the two groups. Interpret the interval estimate.
Part II: Ten adults with symptoms of diabetes were randomly selected and a random blood glucose test was administered before and after a medication. Their blood glucose level readings were gathered before and after the medication and the results are shown below (Values are in the pdf)
(a) Are the samples independent? Justify your answer.
(b) State the appropriate null and alternative hypotheses to test whether the medication has been effective in decreasing blood glucose level.
(c) Calculate the value of the test statistic and test the hypotheses assuming = 0.05.
(d) Find the p-value.
(e) Find a 95% confidence interval for the difference in average blood glucose levels between the two groups. Based on this interval, can one conclude that there is a significant difference in average blood glucose level between the two groups? Justify your answer. Is your finding consistent with that in (c)?
Question 4: The variance in a production process is an important measure of the quality of the process. A large variance often signals an opportunity for improvement in the process by finding ways to remove the process variance. Conduct a statistical test to determine whether there is a significant difference between the variances in the bag weights for the two machines. Use a .05 level of significance. What is your conclusion?
Values for Machine 1: 2.95 3.45 3.50 3.75 3.48 3.26 3.33 3.20 3.16 3.20 3.22 3.38 3.90 3.36 3.25 3.28 3.20 3.22 2.98 3.45 3.70 3.34 3.18 3.35 3.12
Values for Machine 2: 3.22 3.30 3.34 3.28 3.29 3.25 3.30 3.27 3.38 3.34 3.35 3.19 3.35 3.05 3.36 3.28 3.30 3.28 3.30 3.20 3.16 3.33
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