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Category > Management Posted 07 Jul 2017 My Price 13.00

"additional topics in inferential statistics"

Questions for "additional topics in inferential statistics"

I have 3 questions that I need full answers for so that I can understand how the answers were obtained. The questions are:

Question 1: A study is conducted to examine the influence of time spent watching TV or on the internet, on student performance on Statistics exams. A class of 8 students is observed over a period of time, with the independent variable being the total amount of time each student spends on TV/internet, and the dependent variable being their subsequent Statistics exam score, in %. The data is shown in the table below:

 

Student Hrs/week watching TV or on the internet Exam score (%)
1 21 55
2 16 78
3 29 46
4 10 87
5 14 64
6 35 27
7 4 96
8 8

83


(a) Determine the equation of the line of best fit, relating Y = exam score (%) to X = hrs/wk spent watching TV or on the internet.

(b) Use the line of best fit calculated in Part (a) to calculate an estimate for the exam score that a student would get, to the nearest %, if they spent an average of 30 hrs/wk watching TV or on the internet. Repeat for an estimate of the exam score that would result after a student spent an average of 10 hrs/wk watching TV or on the internet.
(c) Plot the raw data from the table on an x-y graph, and then draw the line of best fit showing at least 2 calculated points that are on that line (Hint: your answers for Parts (a) and (b) provide you with 3 such points).

(d) What is the predicted exam score, to the nearest %, for a student who completely avoids the TV or internet? Repeat for a predicted exam score for a student who spends an average of 56 hrs/wk watching TV or on the internet. Comment briefly on your answers for these two estimates, and what it implies about the limitations of the linear regression model generated in Part (a).

e) Conduct a hypothesis test on the significance of correlation between hrs/wk spent watching TV or on the internet, and exam performance, using the critical-value method at LOC = 95%.

(f) Use the p-value method to determine the common values of LOC (if any) for which your decision in Part (e) would be that there is no significant correlation between X and Y, and the common LOC values (if any) for which the opposite decision would be made.


Question 2: A study was undertaken to compare the waste-generating behaviour of residents in four remote, isolated communities: Pétaouchnok, Malakazoo, Erehwon, and Closna. 10 households were randomly selected from each of these communities, and the average daily garbage output measured over a specified period of time. The data obtained is shown in the table below (values in kg/day of waste):

Petaouchnok Malakazoo Erehwon Closna
3.9 1.9 3.5 4.3
3.5 3.2 4.1 4.2
3.6 4.4 1.9 3.6
2.9 4.1 3.6 5.4
2.9 3.1 3.3 4.6
4.1 5.0 2.9 2.7
1.4 4.4 3.7 3.9
4.0 2.0 3.7 5.2
4.2 4.9 2.8 2.8
3.9 3.1 2.9

3.5


a) At LOC = 95%, what would you conclude about whether or not there is any difference in garbage generation rates across these four towns? Use the critical-value method.

b) Using the p-value method, determine if your conclusion from Part (a) would be different for any common values of LOC. 
Question 3: A market gardener grows four different varieties of tomato: cherry, black, plum, and brandywine. A test is conducted whereby 40 seeds of each variety are sown under similar conditions, with the number of germinated and non-germinated seeds recorded. The results are as follows:

   

 

   
Tomato Variety Germinated Non-Germinated
Cherry 19 21 40
Black 33 7 40
Plum 27 13 40
Brandywine 20 20 40
Totals     160
   

a) Conduct a test, at LOC = 95%, for whether the seed germination rate for the market gardener’s tomatoes are independent of, or dependent upon, the particular variety. Use the critical-value method.

b) Using the p-value method, determine if your conclusion from Part (a) would be different for any common values of LOC.

Answers

(5)
Status NEW Posted 07 Jul 2017 09:07 PM My Price 13.00

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