Consider an unbalanced study with six subjects,

identified as A, B, C, D, E and G. In the actual

study,

? Subjects A and B are assigned to the first

treatment, and the other subjects are assigned to the second treatment.

? There are exactly two successes, obtained

by A and C.

This information is needed for parts (a)-(c) below.

(a) Compute the observed value of the test

statistic.

(b) Assume that the Skeptic is correct. Determine the observed value of the test statistic for the assignment that places D and E

on the first treatment, and the remaining

subjects on the second treatment.

(c) We have obtained the sampling distribution of the test statistic on the assumption

that the Skeptic is correct. It also is possible to obtain a sampling distribution of the

test statistic if the Skeptic is wrong provided we specify exactly how the Skeptic

is in error. These new sampling distributions are used in the study of statistical

power which is briefly described in Chapter 7 of the text. Assume that the Skeptic

is correct about subjects A and G, but incorrect about subjects B, C, D and E.

For the assignment that puts D and G on

the first treatment, and the other subjects

on the second treatment, determine the response for each of the six subjects.

8. A comparative study is performed; you are

given the following information.

? The total number of subjects equals 33.

? The observed value of the test statistic is

greater than 0.

I used the website to obtain the exact P-value for

Fisher's test for each of the three possible alternatives. These three P-values are below along

with three bogus P-values

A comparative study is performed; you are

given the following information.

? The total number of subjects equals 29.

? The observed value of the test statistic is

greater than 0.

I used the website to obtain the exact P-value for

Fisher's test for each of the three possible alternatives. These three P-values are below along

with three bogus P-values.

Set 1: 0.1445 0.2890 0.9622

Set 2: 0.0762 0.1297 0.9868

(a) Which set contains the correct P-values: 1

or 2? (No explanation is needed.)

(b) For the set you selected in part (a), match

each P-value to its alternative. (No explanation is needed.) Note: Even if you pick

the wrong set in part (a), you can still get

full credit for part (b).

10. A comparative study yields the following numbers: n1 = 10, n2 = 20, m1 = 4 and m2 = 26.

On the assumption the Skeptic is correct, list all

possible values of the test statistic.

11. A balanced CRD is performed with a total of

600 subjects. There is a total of 237 successes,

with 108 of the successes on the first treatment.

Use the standard normal curve to obtain the

approximate P-value for the third alternative

4. Calculation practice: General multiplication rule. In the 1980s in Canada, 52% of adult men smoked. It was estimated that male smokers had a lifetime probability of 17.2% of developing lung cancer, whereas a nonsmoker had a 1.3% chance of getting lung cancer during his life (Villeneuve and Mao 1994).8 a. What is the conditional probability of a Canadian man getting cancer, given that he smoked in the 1980s? b. Draw a probability tree to show the proba- bility of getting lung cancer conditional on smoking. c. Using the tree, calculate the probability that a Canadian man in the 1980s both smoked and eventually contracted lung cancer. d. Using the general multiplication rule, cal- culate the probability that a Canadian man in the 1980s both smoked and eventually contracted lung cancer. Did you get the same answer as in (c)? e. Using the general multiplication rule, calcu- late the probability that a Canadian man in the 1980s both did not smoke and never con- tracted lung cancer.The folowing concepts mathematically and give some examples (numerically) which are necessary in probability theory event sample sponce - statistical inference descriptive s. permutasyou kon binasyon - clensity function - conditional probability - multiplication rule - dependent event - Independent event Boyes Rule . P.s ; The find and discuit the validated of Bayes' Rule .3. Drake Marketing and Promotions has randomly surveyed 200 men who watch professional sports. The men we're separated according to their educational level (college degree or not) and whether they preferred the NBA or the NFL. The results are shown below: College Degree No College Degree Totals Prefer NBA 40 55 95 Prefer NFL 10 95 105 Totals 156 200 It might help to start by making a new column and row for totals. (a) What is the probability that a randomly selected survey participant prefers the NEL? 105 200 (b] What is the probability that a randomly selected survey participant has a college degree and prefers the NBA?. 95 (c) Suppose a survey participant is randomly selected and you are told that he has a college degree. What is the conditional probability that this man prefers the NFL? (d) Are the two events, "College degree" and "Prefer NFL" independent? (Justify your answer] 4. Find the following probabilities using multiplication rules and conditional probability definitions. (a) Suppose that E and F are two events and that P(E and F) = _6 and P(E) = .8. What is P(FIE]? (b) Suppose that E and F are two events and that P(E) = 6 and P(FE) = .4. What is P(E and F]? (c] Suppose that E and F are two events and that P[E and F) = .4 and P(FIE) = .6. What Is P(E]?Section 4.3: The Multiplication Rules and Conditional Probability. Two events A and B are independent events if the fact that A occurs does not affect the probability of B occurring When the outcome or occurrence of the first event affects the outcome or occurrence of the second event in such way that the probability is changed, the events are said to be dependent events. Example # 19: Determine whether these events are dependent or independent a) Tossing a coin and drawing a card from a deck. b) Drawing a ball from an urn, not replacing it, and then drawing a second ball. c) Drawing a ball from an urn, replacing it, and then drawing a second ball. Multiplication Rule 1 When two events A and B are independent, the probability of both occurring is P(A and B) = P(A)-P(B) Example # 20: A coin is flipped and a die is rolled. Find the probability of getting a head on the coin and a 4 on the die. Example # 21: An urn contains 5 red balls and 3 white balls. A ball is selected and its color noted. Then it is replaced. A second ball is selected and its color noted. Find the probability of each of these. a) Selecting two red balls. b) Selecting two white balls. c) Selecting I red ball and then I white ball. 11