# EBook Problems

## Probability and Statistics EBook Practice Problems

The problems provided below may be useful for practicing the concepts, methods and analysis protocols, and for self-evaluation of learning of the materials presented in the EBook.

# II. Describing, Exploring, and Comparing Data

## Pictures of Data

1. Two random samples were taken to determine backpack load difference between seniors and freshmen, in pounds. The following are the summaries:

 Year Mean SD Median Min Max Range Count Freshmen 20.43 4.21 17.20 5.78 31.68 25.9 115 Senior 18.67 3.56 18.67 5.31 27.66 22.35 157

Which of the following plots would be the most useful in comparing the two sets of backpack weights?

A. Histograms

B. Dot Plots

C. Scatter Plots

D. Box Plots

## Measures of Central Tendency

1. Suppose that in a certain country, the average yearly income for 75% of the population is below average, what would you use as the measure of center and spread?

A. Mean and interquartile range

B. Mean and standard deviation

C. Median and interquartile range

D. Mean and standard deviation

## Measures of Variation

1. The number of flaws of an electroplated automobile grill is known to have the following probability distribution:

 X 0 1 2 3 P(X) 0.8 0.1 0.05 0.05

What would be the standard deviation of the sample means if we took 100 samples, each sample with 200 grills, and computed their sample means?

A. 0.6275

B. 0.0560

C. None of the Above

D. 0.89269

2. Suppose that in a certain country, the average yearly income for 75% of the population is below average, what would you use as the measure of center and spread?

A. Mean and interquartile range

B. Mean and standard deviation

C. Median and interquartile range

D. Mean and standard deviation

# III. Probability

## Rules for Computing Probabilities

1. A professor who teaches 500 students in an introductory psychology course reports that 250 of the students have taken at least one introductory statistics course, and the other 250 have not taken any statistics courses. 200 of the students were freshmen, and the other 300 students were not freshmen. Exactly 50 of the students were freshmen who had taken at least one introductory statistics course.

If you select one of these psychology students at random, what is the probability that the student is not a freshman and has never taken a statistics course?

A. 30%

B. 40%

C. 50%

D. 60%

E. 20%

# IV. Probability Distributions

## Expectation(Mean) and Variance)

1. Ming’s Seafood Shop stocks live lobsters. Ming pays \$6.00 for each lobster and sells each one for \$12.00. The demand X for these lobsters in a given day has the following probability mass function.

 X 0 1 2 3 4 5 P(x) 0.05 0.15 0.3 0.2 0.2 0.1

What is the Expected Demand?

A. 13.5

B. 3.1

C. 2.65

D. 5.2

# VIII. Hypothesis Testing

## Fundamentals of Hypothesis Testing

1. Suppose you were hired to conduct a study to find out which of two brands of soda college students think taste better. In your study, students are given a blind taste test. They rate one brand and then rated the other, in random order. The ratings are given on a scale of 1 (awful) to 5 (delicious). Which type of test would be the best to compare these ratings?

A. One-Sample t

B. Chi-Square

C. Paired Difference t

D. Two-Sample t

2. USA Today's AD Track examined the effectiveness of the new ads involving the Pets.com Sock Puppet (which is now extinct). In particular, they conducted a nationwide poll of 428 adults who had seen the Pets.com ads and asked for their opinions. They found that 36% of the respondents said they liked the ads. Suppose you increased the sample size for this poll to 1000, but you had the same sample percentage who like the ads (36%). How would this change the p-value of the hypothesis test you want to conduct?

A. No way to tell

B. The new p-value would be the same as before

C. The new p-value would be smaller than before

D. The new p-value would be larger than before

# X. Correlation and regression

## Correlation

1. A positive correlation between two variables X and Y means that if X increases, this will cause the value of Y to increase.

A. This is always true.

B. This is sometimes true.

C. This is never true.

2. The correlation between high school algebra and geometry scores was found to be + 0.8. Which of the following statements is not true?

A. Most of the students who have above average scores in algebra also have above average scores in geometry.

B. Most people who have above average scores in algebra will have below average scores in geometry

C. If we increase a student's score in algebra (ie. with extra tutoring in algebra), then the student's geometry scores will always increase accordingly.

D. Most students who have below average scores in algebra also have below average scores in geometry.