IIMT 1640 HW4
Total Points: 100 Due Date: 10pm, 28 April.
• Write down the detail calculation to receive full mark.
• For the questions below, please keep 3 decimal places.
• Scan the hand-written homework as a PDF, combined with the functions,
outputs and figures produced by Excel. In the end, submit the combined PDF on Moodle.
1. A diet doctor claims that the average North American is more than 20 pounds over- weight. To test his claim, a simple random sample of 20 North Americans was weighted, and the difference between their actual weight and their ideal weight was calculated. The data are listed here. Assume the population is normally distributed. Formulate the null and alternative hypothesis, and test at the 5% significance level. (14pts)
26 19 23 15 16 17 15 16 35 18
16 23 18 41 22 18 23 19 22 15
(a) Use the critical value approach.
(b) Use the p-value approach (Hint: to compute the right-tail probability in t distribution in Excel, you can use T.DIST.RT function(x, df), where “x” is the value for which you want to calculate the right-tail probability and “df” is the degrees of freedom).
2. Consider the following hypotheses for the population proportion,
H0 : p = 0.65 vs Ha : p ≠0.65.
Suppose that the sample proportion iŝ(p) = 0.7 and the sample size n = 300. Perform the test at the 10% significance level. (13pts)
(a) Use the critical value approach.
(b) Use the p-value approach.
3. The following table summarizes whether the stock market went up or down during each trading day of 2010. Suppose this is a simple random sample. Let us suppose the significance level α=0.05. (14pts)
|
|
Day of Week
|
|
Monday
|
Tuesday
|
Wednesday
|
Thursday
|
Friday
|
|
Market Direction
|
Down
|
42
|
49
|
46
|
43
|
41
|
|
Up
|
53
|
55
|
58
|
59
|
58
|
(c) Does the data table meet the conditions required by the Chi-square test for independence?
(d) Use a Chi-square test to determine if these data indicate that trading on some days is better or worse (more or less likely to earn positive returns) than any other. In other words, conduct a Chi-square test for independence between the two variables.
4. A large company employs several thousand people in the manufacture of keyboards, equipment cases, and cables for the computer industry. The personnel manager of the company would like to find ways to forecast the absentee rate among the company employees. An effective method of forecasting would greatly strengthen the ability to plan properly. He took a sample of 15 employees and recorded the number of absent days (Y) during the last fiscal year along with employee age (X). The computer output of a regression analysis is as follows. (25pts)
(a) An employee, John, is 30 years old. According to the regression equation, what is his expected number of absent days in the coming fiscal year? (Note: 30 is within the range of age in the dataset, and do NOT round the days to integers)
(b) Instead of our regular testing for whether β1 is 0 or not, can you conduct a test, such that the alternative hypothesis is: the regression coefficient β1 is larger than 0.2. Test at 5% significance level. Hint: the SE of b1 will not change, only the numerator in the t-statistic will be changed to (b1-0.2).
(c) Find a 95% confidence interval for the regression coefficient of age, β1 .
(d) The sample mean and sample standard deviation for age (X) are 37.87 and 10.39, respectively. Find a 95% confidence interval for the mean absent days of 30 years old employees.
(e) The sample mean and sample standard deviation for age (X) are 37.87 and 10.39, respectively. Find a 99% prediction interval for the absent days of 30 years old employees.
5. An ardent fan of television game shows has observed that, in general, the more educated the contestant, the less money he or she wins. To test her belief, she gathers data about the last eight winners of her favorite game show. She records their winnings in dollars and the number of years of education. The results are as follows:
Note: [Please write down all the formula and create tables in Excel for computation, to receive full points. Please copy the full table for HW submission.] (34pts)
(a) Find the slope b1 and the intercept b0 of the least squares regression line.
(b) Use the regression line in (a) to estimate the average winnings when Years of Education is 5. Do you believe in this estimate? Explain briefly using knowledge from regression analysis.
(c) Interpret the slope coefficient b1 specifically in terms of this problem.
(d) Determine the standard error estimate s.
(e) Determine the coefficient of determination R2, and discuss what its value tells you.
(f) Calculate the correlation coefficient. What sign does it have? Does it match with the sign of b1? What does it mean in the context of this problem?