Assignment 2
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Assignment 2
Please use programming to solve the following problems!
Please attach your code and the corresponding output!
1. In order to study student’s height in a certain high school, the following data is collected.
|
Male |
Female |
|
155.2 |
150.1 |
|
158.7 |
152.9 |
|
159.2 |
153.4 |
|
162.1 |
153.9 |
|
163.2 |
154.2 |
|
164.3 |
156.6 |
|
164.6 |
158.0 |
|
165.9 |
158.1 |
|
167.2 |
158.3 |
|
167.5 |
158.6 |
|
168.3 |
159.8 |
|
170.5 |
160.2 |
|
172.6 |
161.1 |
|
177.5 179.7 |
161.4 |
(a) Assume that the population of female is normal. Construct a 95% two-sided confidence interval for the
variance of female’s population.
(b) Assume that the population of female is normal. Construct a 95% lower one-sided confidence interval
for the mean of female’s population.
(c) Use Wilcoxon signed-rank test to test whether the median of female’s population is 154 under 5% significant level. [Hint: use signrank function in Matlab].
(d) Assume that the population of male and female are normal. Test whether two populations have the same variance under 10% significant level.
(e) Based on (d), test whether male have a larger mean in height than female under 10% significant level.
(f) Based on (d), construct a 95% two-sided confidence interval for the difference between two population
means.
(g) Use Wilcoxon rank-sum test to test whether male and female populations have the same median under
5% significant level. [Hint: use ranksum function in Matlab]. (40 marks)
2. The following table presents a study on the payment received by 18 faculty members for teaching a course in a large metropolitan university.
|
Subject Matter |
Payment |
|||||
|
Humanities Social Science Engineering |
2.0 |
2.3 |
2.7 |
2.6 |
2.8 |
3.1 |
|
2.6 |
2.9 |
3.3 |
3.5 |
3.8 |
3.9 |
|
|
2.7 |
3.0 |
3.7 |
2.8 |
3.0 |
3.5 |
|
(a) Construct a one-way analysis table and comment on it based on 5% significant level.
(b) Perform Bonferroni method at 5% significance level to determine which pairs of subjects differ in their
means. Use Matlab to get tα if necessary. (16 marks)
3. Suppose that a credit company would like to investigate the relationship between expense of credit card per month & annual income of young people
20 people are randomly selected, their expense and income are given below.
|
Expense (夕) |
1.217 |
1.252 |
0.857 |
1.022 |
0.816 |
0.951 |
0.934 |
0.703 |
0.968 |
0.655 |
|
Income (α) |
16.0 |
15.8 |
11.5 |
13.4 |
10.0 |
11.7 |
11.8 |
9.0 |
16.3 |
8.2 |
|
Expense (夕) |
0.802 |
1.125 |
0.752 |
0.692 |
0.725 |
0.642 |
0.683 |
0.527 |
0.553 |
0.690 |
|
Income (α) |
10.3 |
16.9 |
9.8 |
8.4 |
9.6 |
7.9 |
8.4 |
7.4 |
6.7 |
8.5 |
Expense and Income are reported in X104 RMB.
(a) Draw a scatter plot and comment on it. [Hint: use scatter function in Matlab].
(b) Estimate the regression line μY |北 = β0 + β1 α; construct 95% two-sided confidence intervals for β0 and β 1 ; report ∩2 and comment on it.
(c) If the regression line in (b) is used, check the normality of residuals.
(d) Estimate the mean value of Y when α = 10．5, and construct a 95% two-sided confidence interval for it. (e) Construct a 95% two-sided prediction interval for Y when α = 10．5. (44 marks)
2023-01-02