## Stats

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The following applies to Questions 1 to 3.

A box contains four numbered balls (1, 1, 2, and 3). We will randomly select two balls from the box (without replacement).

(Hint: since the selections are without replacement, this means, for example, that if the ball labelled “2” is selected on the first selection, it can not be selected again on the second selection.

Question 1 (1 point)

Description: uestion 1 Saved

The outcome of interest is the number on each of the two balls we select. How many outcomes are contained in the sample space?

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Question 2 (2 points)

Description: uestion 2 Saved

Let X be the sum of the two numbers on the selected balls. Find the probability distribution of X.

In the following four blanks, enter your answers as fractions in the following order: P(X = 2), P(X = 3), P(X = 4), and P(X = 5).

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Question 3 (2 points)

Description: uestion 3 Saved

What is the probability that X = 3 if we know that the first selection is not a “3”?

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The following applies to Questions 4 to 6.

A survey of the members of a magazine club revealed the following results:

· 4% read all three magazines

We will randomly select one member of the magazine club.

Question 4 (1 point)

Description: uestion 4 Saved

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Question 5 (1 point)

Description: uestion 5 Saved

What is the probability that the selected person reads Maclean’s if we know they don’t read Reader’s Digest?

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Question 6 (1 point)

Description: uestion 6 Saved

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The following information about a deck of cards applies to Questions 7 and 8.

A standard deck of cards consists of 52 cards. There are 13 cards (2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, Ace) in each of four suits (Clubs, Diamonds, Hearts, and Spades).

Question 7 (1 point)

Description: uestion 7 Unsaved

You randomly select 3 cards without replacement. Let S1 be the event that the first card is a spade, let S2 be the event that the second card is a spade, and let S3 be the event that the third card is a spade. What is PS3(Sc1 Intersection Sc2)?

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Question 8 (1 point)

Description: uestion 8 Unsaved

You randomly select one card from a deck of cards. Let A be the event that the selected card is an Ace and let H be the event that the selected card is a heart. Are the events A and H independent? Explain why or why not.

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The following applies to Questions 9 and 10.

Let the probability distribution of X be given as follows:

xi

1

2

3

pi

0.2

0.3

0.5

Question 9 (1 point)

Description: uestion 9 Unsaved

What is the expected value of X?

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Question 10 (1 point)

Description: uestion 10 Unsaved

What is the variance of X?

Keep all decimal places in intermediate calculations and enter your answer as a decimal.

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Question 11 (2 points)

Description: uestion 11 Unsaved

Scores on the Math portion of a college entrance exam are normally distributed with mean 530 and standard deviation 70. Scores on the Verbal portion of the same exam are normally distributed with mean 475 and standard deviation 75. What is the probability that a randomly selected Math score is greater than a randomly selected Verbal score?

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Question 12 (2 points)

Description: uestion 12 Unsaved

Quiz scores in a Statistics class follow a normal distribution mean 70 and standard deviation 10.

In a random sample of 10 students from the class, what is the probability that at least 1 student has a quiz score above 85?

(Hint: first find the probability that one randomly selected student has a quiz score above 85. Then use this answer to answer the above question.)

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Question 13 (2 points)

Description: uestion 13 Unsaved

Trees are distributed in a large forest according to a Poisson distribution with a rate of 0.2 per square meter. If we randomly select a circular area of the forest with a radius of 3 meters, what is the probability this area will contain 5 trees? (Area of a circle = pr2{“version”:”1.1″,”math”:”pi r^2″})

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Question 14 (1.5 points)

Description: uestion 14 Unsaved

We would like to conduct a hypothesis test at the 10% level of significance to determine if the true proportion of Canadians who are left-handed differs from 0.10. A random sample of 200 Canadians is selected. What is the rejection rule in terms of pÌ‚ {“version”:”1.1″,”math”:”hat{p}”}?

(You do not need to show your work. Just give the final answer. You can write pÌ‚ {“version”:”1.1″,”math”:”hat{p}”} as “p-hat” to avoid using the Graphical Equation Editor.)

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Question 15 (2 points)

Description: uestion 15 Unsaved

Question 15 options:

We would like to compare the current unemployment rates in Canada and the U.S. In a random sample of 400 Canadians, 28 of them are found to be unemployed. In a random sample of 300 Americans, 15 are unemployed. Calculate a 94% confidence interval for the true difference in proportions of Canadian and American adults that are unemployed (pC – pA).

Keep 6 decimal places in intermediate calculations and report your final answer to 3 decimal places.

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The following applies to Questions 16 – 19.

We would like to compare the grade distributions for three different science courses at a large university. Random samples are selected from first-year biology, chemistry, and physics courses and their final grades are summarized in the table below, as well as some expected cell counts and some cell chi-square values:

Observed

Expected

Cell Chi-Square

Biology

Chemistry

Physics

Row

Total

A+

17

20.9

0.72

25

20.3

1.09

18

18.8

0.04

60

A

32

24.0

2.66

22

23.3

0.08

15

21.6

2.04

69

B+

24

20.5

0.59

18

20.0

0.19

17

18.5

0.12

59

B

38

32.0

1.12

28

31.1

0.32

26

28.9

0.28

92

C+

18

19.8

0.17

20

19.3

0.03

19

17.9

0.07

57

C

31

33.4

0.17

34

32.5

0.07

31

30.1

0.03

96

D

16

18.8

0.41

17

18.3

0.09

21

16.9

0.97

54

F

7

13.6

3.18

14

13.2

0.05

18

???

???

39

Column Total

183

178

165

526

Question 16 (1 point)

Description: uestion 16 Unsaved

What are the appropriate hypotheses to test?

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Question 17 (1 point)

Description: uestion 17 Saved

What is the decision rule for testing the hypotheses in Question 16 using the critical value method with a 1% level of significance?

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Question 18 (1 point)

Description: uestion 18 Unsaved

What is the appropriate test statistic?

(To save you time, the sum of the 23 cell chi-square values that are given (excluding the one missing value) is 14.49.)

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Question 19 (1 point)

Description: uestion 19 Saved

What is the conclusion of the hypothesis test at the 5% level of significance?

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The following applies to Questions 20 and 21.

Three contestants compete on each episode of the TV game show Jeopardy!. The number of female contestants for a random sample of 100 episodes are shown in the table below:

# of females

0

1

2

3

# of episodes

45

35

15

5

Question 20 (4 points)

Description: uestion 20 Saved

Conduct a chi-square goodness of fit test at the 5% level of significance to determine whether the number of female contestants per episode follows a binomial distribution with parameter p = 0.25.

Show all of your work. The conclusion of the hypothesis test is partially pre-filled. Edit/add to the answer.

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Question 21 (1 point)

Description: uestion 21 Unsaved

What would be the estimated value of the parameter p if we didn’t want to make an assumption about its value?