Stat 1350 - Elementary Statistics

Jigsaw Review for Test 2

Chapters 14-15 and 17-20

Group 1 - Regression - Chapters 14-15:

1. From Rex Boggs in Australia comes an unusual data set: before showering

in the morning, he weighed the bar of soap in his shower stall. The weight

goes down as the soap is used. The data appear in Table II.3 (weights in

grams). Notice that Mr. Boggs forgot to weigh the soap on some days.

[pic]

A. Plot the weight of the bar of soap against day. [pic] [pic]

B. Is the overall pattern roughly straight-line? Based on your

scatterplot, is the correlation between day and weight close to 1,

positive but not close to 1, close to 0, negative but not close to -1,

or close to -1? Explain your answer.

The overall pattern is roughly straight-line. The correlation would

be close to -1 since the points are very close to lying on a straight

decreasing line.

C. Find the equation for the least-squares regression line for the data

in Table II.3 and write it below. Draw the regression line on your

scatterplot from the previous exercise.

y = 133.18 - 6.31x

1) Explain carefully what the slope b = -6.31 tells us about how fast

the soap lost weight.

Every day the weight of the soap decreases 6.31 grams.

2) Mr. Boggs did not measure the weight of the soap on Day 4. Use the

regression equation to predict that weight.

y = 133.18 - 6.31(4) = 107.94 grams

3) Use the regression equation in the previous exercise to predict the

weight of the soap after 30 days. Why is it clear that your answer

makes no sense? What\'s wrong with using the regression line to

predict weight after 30 days?

After 30 days the soap would weigh - 56.12 grams which is physically

impossible. Extrapolation is risky!!!

Group 2 - Probability - Chapters 17-20

1 Choose a student at random from all who took Stats 1350 in recent years.

The probabilities for the student\'s grade are

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a) What must be the probability of getting an F?

b) What is the probability that a student will fail the class (earn D or

F)?

c) If you choose 5 students at random from all those who have taken Stats

1350, what is the probability that all the students chosen got a B or

better?

d) To simulate the grades of randomly chosen students, how would you

assign digits to represent the five possible outcomes listed?

e) Use lines 101-102 from the Random Number Table to simulate 10

repetitions of randomly choosing 5 students and use your results to

estimate the probability that all five students chosen got a B or

better. How does this compare to the probability you calculated in

part (c)? Explain.

2. Rotter Partners is planning a major investment. The amount of profit X

is uncertain, but a probabilistic estimate gives the following distribution

(in millions of dollars):

[pic]

What is the expected value of the profit?

Interpret this value in a complete sentence in the context of the problem.

Group 3 - Probability - Chapters 17-20 (continued)

1. Choose a student in grades 9 to 12 at random and ask if he or she is

studying a language other than English. Here is the distribution of

results:

[pic]

a) Explain why this is a legitimate probability model.

b) What is the probability that a randomly chosen student is studying

a language other than English?

(c) What is the probability that a randomly chosen student is

studying French, German, or Spanish?

2. Abby, Deborah, Mei-Ling, Sam, and Roberto work in a firm\'s public

relations office. Their employer must choose two of them to attend a

conference in Paris. To avoid unfairness, the choice will be made by

drawing two names from a hat. (This is an SRS of size 2.)

(a) Write down all possible choices of two of the five names. These are the

possible outcomes.

(b) The random drawing makes all outcomes equally likely. What is the

probability of each outcome?

(c) What is the probability that Mei-Ling is chosen?

(d) What is the probability that neither of the two men (Sam and Roberto)

is chosen?

Group 4 - Probability - Chapters 17-20 (continued)

1. Are Americans interested in opinion polls about the major issues of the

day? Suppose that 40% of all adults are very interested in such polls.

(According to sample surveys that ask this question, 40% is

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