Microsoft Word - STAT Assignment
1. Anationalrepresentativesurveyofstudentsingrades7-12askedaboutthe experience of these students with respect to sexual harassment. The students were asked whether or not they were harassed in person and whether or not they were harassed online. Here are the data for the boys:
1. (a) What is the sample proportion of being harassed in person given being harassed online? (call it ????") What is the sample proportion of being harassed in person given not being harassed online? (call it ????#)
2. (b) Is there a difference between the two sample proportions? (Conduct a two sample proportion test with significance level 0.05)
3. (c) Is there an association between being harassed online and in person? (significant level 0.05)
(d) What do you find when you compare your statistics in part (b) and (c)? [Check the squared z statistic in part (b)]
2. APewInternetsurveyaskedcollegepresidentswhetherornottheybelieved that online courses offer an equal educational value when compared with courses taken in the classroom. The presidents were classified by the type of educational institution. Here are the data:
(a) Show the distribution of response using barplots for each of the institution type. (?barplot in R, check the argument ‘beside')
(b) Is there an association between the presidents' opinion to the question above with their institution types? (significant level 0.05)
Harassed in person Harassed online
|
Harassed in person
|
Harassed online
|
|
Yes
|
No
|
|
Yes
|
183
|
154
|
|
No
|
48
|
578
|
|
Response
|
Institution Type
|
|
4-year private
|
4-year public
|
2-year private
|
For profit
|
|
Yes
|
36
|
50
|
66
|
54
|
|
No
|
62
|
48
|
34
|
45
|
3. Asurveyof13,691Canadianstudentswhoenrolledinprivatecareercolleges was conducted to understand student participation in the private postsecondary education system. Students were asked about their field of study and how they paid for their education. A major source of funding was government loans. Here are the survey percents of Canadian private students who use government loans to finance their education by field of study:
|
Field of study
|
Number of students
|
Percent using government loans
|
|
Trades
|
942
|
45%
|
|
Design
|
599
|
53%
|
|
Health
|
5234
|
55%
|
|
Media/IT
|
3238
|
55%
|
|
Service
|
1378
|
60%
|
|
Other
|
2300
|
47%
|
1. (a) Construct the 6 by 2 table of counts from above table. (No need to round up to integers)
2. (b) Test the null hypothesis that the percent of students using government loans to finance their education does not vary with field of study. What is your conclusion? (significant level 0.05)
4. RecalltheexampleoflongleafpinetreesintheWadeTract.Wewantto examine whether the distribution of trees in the tract is random or not. First, we divide the tract into four equal parts, or quadrants, in the east-west direction. Call the four pars Q1 to Q4. Then we take a random sample of trees and count the number of trees in each quadrant. Here are the data:
1. (a) If the trees are randomly distributed, we expect to find 26 trees in each quadrant. Why? Explain your answer.
2. (b) However, we do not really expect to get exactly 26 trees in each quadrant. Why?
3. (c) Perform the goodness-of-fit test for these data to determine if these trees are randomly scattered. What is your conclusion. (significant level 0.05)
|
Quadrant
|
Q1
|
Q2
|
Q3
|
Q4
|
|
Count
|
40
|
18
|
24
|
22
|
5. Kiplinger's"BestValuesinPublicColleges"providesarankingofU.S.public colleges based on a combination of various measures of academics and affordability. We'll consider a random collection of 40 colleges from Kiplinger's 2011-2012 report and focus on the average debt in dollars at graduation (AvgDebt) and the percent of students who borrow (PercBorrow). Below is the output from R for the simple linear regression of AvgDebt on PercBorrow.
1. (a) State the least-squares regression line.
2. (b) Construct a 95% confidence interval for the slope. What does this interval tell you about the change in average debt for a change in the percent who borrow?
3. (c) At Miami University, 51% of the students borrow, and the average debt is $27,315. What is the residual?
A national representative survey of students in grades 7-12 asked about the experience of these students with respect to sexual harassment. The students were asked whether or not they were harassed in person and whether or not they were harassed online. Here are the data for the boys: Harassed online Harassed in person Yes No Yes 183 154 No 48 578
(a) What is the sample proportion of being harassed in person given being harassed online? (call it " ) What is the sample proportion of being harassed in person given not being harassed online? (call it # )
(b) Is there a difference between the two sample proportions? (Conduct a two sample proportion test with significance level 0.05)
(c) Is there an association between being harassed online and in person? (significant level 0.05)
(d) What do you find when you compare your statistics in part (b) and (c)? [Check the squared z statistic in part (b)]
2. A Pew Internet survey asked college presidents whether or not they believed that online courses offer an equal educational value when compared with courses taken in the classroom. The presidents were classified by the type of educational institution. Here are the data: Response Yes No 4-year private 36 62 Institution Type 4-year public 2-year private 50 66 48 34 For profit 54 45
(a) Show the distribution of response using barplots for each of the institution type. (?barplot in R, check the argument ‘beside')
(b) Is there an association between the presidents' opinion to the question above with their institution types? (significant level 0.05)
3. A survey of 13,691 Canadian students who enrolled in private career colleges was conducted to understand student participation in the private postsecondary education system. Students were asked about their field of study and how they paid for their education. A major source of funding was government loans. Here are the survey percents of Canadian private students who use government loans to finance their education by field of study: Field of study Number of students Percent using government loans Trades 942 45% Design 599 53% Health 5234 55% Media/IT 3238 55% Service 1378 60% Other 2300 47%
(a) Construct the 6 by 2 table of counts from above table. (No need to round up to integers)
(b) Test the null hypothesis that the percent of students using government loans to finance their education does not vary with field of study. What is your conclusion? (significant level 0.05)
4. Recall the example of longleaf pine trees in the Wade Tract. We want to examine whether the distribution of trees in the tract is random or not. First, we divide the tract into four equal parts, or quadrants, in the east-west direction.
Call the four pars Q1 to Q4. Then we take a random sample of trees and count the number of trees in each quadrant. Here are the data: Quadrant Q1 Q2 Q3 Q4 Count 40 18 24 22
(a) If the trees are randomly distributed, we expect to find 26 trees in each quadrant. Why? Explain your answer.
(b) However, we do not really expect to get exactly 26 trees in each quadrant. Why?
(c) Perform the goodness-of-fit test for these data to determine if these trees are randomly scattered. What is your conclusion. (significant level 0.05)
5. Kiplinger's "Best Values in Public Colleges" provides a ranking of U.S. public colleges based on a combination of various measures of academics and affordability. We'll consider a random collection of 40 colleges from Kiplinger's 2011-2012 report and focus on the average debt in dollars at graduation (AvgDebt) and the percent of students who borrow (PercBorrow). Below is the output from R for the simple linear regression of AvgDebt on PercBorrow.
(a) State the least-squares regression line.
(b) Construct a 95% confidence interval for the slope. What does this interval tell you about the change in average debt for a change in the percent who borrow?
(c) At Miami University, 51% of the students borrow, and the average debt is $27,315. What is the residual?