Ger1000: Quiz 9

GER QUIZ 9 (REVISION QUIZ 1)

1) Players can spend $1 to play a lottery game, which has 7 prizes in total. The prize amount and the corresponding chance of winning the prize have been summarized in the following table. Suppose net profit is defined as winnings subtracted by cost. What is the average net profit of playing this game? (choose the closest one)

Answer: -0.55

Solution: Expected Winnings: (1 500 000 / 14 000 000) + (100 000 / 2 330 000) + (2 000 / 55 500) + (350 / 22 200) + (50 / 1080) + (25 / 810) + (10 / 60) = 0.446
Expected Net Profit = -1 + 0.446 = -0.554 = - 0.55

2) Some scientists have found that drinking coffee is associated with students’ ability to sleep (enough vs not enough sleep). Sex was a confounder. This means that:
(I) Percentage of coffee drinkers among males is different from the percentage of coffee drinkers among females.
(II) Percentage of males among coffee drinkers is different from the percentage of females among coffee drinkers.
(III) Percentage of males among students who have enough sleep is different from the percentage of males among students who do not have enough sleep.

Answer: (I) and (II) only

Solution: Self-Explanatory.

3) In the Hunger Game, four families are involved and each family has two children. The details are as follows. One child will be randomly selected from the 8 children of the 4 families.
What is the probability that he is the younger one in the family, if the selected child is a boy?

Answer: 1/2

Solution: P(Boy) = 4/8 = 0.50
P(Younger AND Boy) = 2/8 = 0.25
P(Younger | Boy) = P(Younger AND Boy) | P(Boy) = 0.25 / 0.5 = 1/2

4) Suppose you want to measure the build quality of an industrial product. The factory has manufactured 200 batches, with 8 units per batch, for a total of 1600 units. You decide to sample 80 of the units. Suppose you randomly sample 10 batches and then select every unit in those 10 batches to be in your sample, for a total of 80 units. What kind of sample have you obtained?

Answer: A systematic sample

Solution: Self-Explanatory

5) 100,000 women were encouraged to do annual screening for breast cancer; 40,000 accepted, but 60,000 refused. After 5 years, death rates from breast cancer (per 10,000) were 1.1 for the women who were screened, and 2.5 for the women who refused. It is known that poorer women were less likely to accept screening than richer ones, and that breast cancer affects the rich more than the poor.
To show that screening reduces the risk from breast cancer, someone wants to compare the death rates from breast cancer among the screening group and the non-screening group, which are 1.1 and 2.5, respectively. Only based on the given information, 2.5 – 1.1 = 1.4 is likely ______ of the reduction in death rate from breast cancer due to screening.

Answer: an overestimate

Solution: Given death rate is 1.1 among thr 40,000 who accepted screening and 2.5 among the 60,000 who refused screening. By changing the ratio of those who accepted screening, there are 1.65 among the "60,000" who accepted screening and thus answer should be 2.5 - 1.65 = 0.85
Given that 1.4 > 0.85 and that the proportion of those who accepted screening < those who refused it, it should be an overestimate of the reduction in death rate from breast cancer due to screening.