Question 1: Smoking and Lung Cancer
Dr F. E. Tylecote, an English doctor, reported in 1927 that almost every lung cancer patient he had known about had been a smoker. And in 1936 two more doctors (Arkin and Wagner) reported that 90% of 135 men afflicted with lung cancer were chronic smokers.
In these studies what do you think was the target population?
What type of quantitative studies are these? Explain.
If we want to determine the level of the association between smoking and lung cancer, what other information is required? Hence state what type of quantitative study is required.
How would you carry out a following type of study for investigating the relation between cigarette smoking and lung cancer? For each type of study write around 4 to 6 sentences.
A case-control study
A cohort study
Question 2
In the sport of archery in Question 2 of Assignment 1(please refer to another attached doc), scores are awarded depending upon the accuracy of the shot. Over a long period of time, a particular competitor has made scores according to the proportions in the table below.
Score Proportion of times
100 (bullseye) 0.10
50 0.25
25 0.30
10 0.10
0 0.25
If the above proportions represent the probability that the competitor will achieve that score with a single shot, and the shots are considered to be independent, answer the following questions.
What are the expected (mean) score of the competitor with a single shot and the standard deviation of the competitor's scores from assignment 1 (please refer to another attached doc)?
Find a 95% probability interval for the total score of the competitor if they have a total of 150 shots.
During the preliminary game leading up to 2016 Rio de Janerio Olympics, the competitor has 50 shots with the frequency of results shown in the table below.
|
Outcome
|
100 (Bullseye)
|
50
|
25
|
10
|
0
|
|
No. of times
|
12
|
22
|
5
|
9
|
2
|
Use an appropriate statistical test (clearly state what the test is) to determine whether the competitor seemed to be performing differently than in previous seasons. Determine the p-value for your test statistic as well as the 5% critical value for the test. Try to write down the Microsoft Excel commands.
Use: 2 sample t-test, chi-squared goodness of fit test or chi-squared test of independence
Question 3
Consider the "roll of the two cylinders" game in Question 3 of Assignment 1 (please refer to other attached doc) where two of five faced regular cylinders are rolled independently. Recall that the player's score is the total on the two outcomes where the outcome of a roll is the number on the side in contact with the table. The casino charges players $6.50 to play the game (every roll of the two cylinders) and the return to the player is their score (in $).
Table below may be helpful
Probability distribution of return after one throw of the two cylinders
|
y
|
$2
|
$3
|
$4
|
$5
|
$6
|
$7
|
$8
|
$9
|
$10
|
|
Pr(X=x)
|
1/25 =0.04
|
2/25 =0.08
|
3/25 =0.12
|
4/25 =0.16
|
5/25 =0.20
|
4/25 =0.16
|
3/25 =0.12
|
2/25 =0.08
|
1/25 =0.04
|
A player starts the evening with $500 and play this game 36 times. Determine the following.
A 95% probability interval (to the nearest $) for the total amount of money the player will have returned to her after the 36 games.
A 95% probability interval for the amount of money that the player will take home with her.
What is the player's chance of being ahead after playing this game 50 times?
Calculate at least how many plays of the game are required such that the chance of the player being ahead is less than 1%.
Question 4
"With whom do you find it easier to make friends?"
A counsellor at a University claims that, when asked this question, 30% of students will say that they find it easier to make friends with the same sex, 20% with the opposite sex and the rest will claim that it makes no difference.
The figures below show a sample collected by a keen Statistics student at the university. Use the Chi squared goodness of fit test (clearly state the relevant hypotheses are) to test the counselor's claim. Use Microsoft Excel to determine the p-value for your test statistic as well as the 5% critical value for the test. Try to write down the Microsoft Excel commands.
|
Friends
|
Number of students
|
|
Same sex
|
24
|
|
Opposite sex
|
21
|
|
No difference
|
55
|