EBook Problems

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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.

I. Introduction to Statistics

The Nature of Data and Variation

Uses and Abuses of Statistics

Design of Experiments

Statistics with Tools (Calculators and Computers)

II. Describing, Exploring, and Comparing Data

Types of Data

Summarizing Data with Frequency Tables

Pictures of Data

Measures of Central Tendency

Measures of Variation

Measures of Shape


Graphs and Exploratory Data Analysis

III. Probability


Rules for Computing Probabilities

Probabilities Through Simulations


IV. Probability Distributions

Random Variables

Expectation(Mean) and Variance)

Bernoulli and Binomial Experiments

Multinomial Experiments

Geometric, Hypergeometric, and Negative Binomial

Poisson Distribution

V. Normal Probability Distribution

The Standard Normal Distribution

Nonstandard Normal Distribution: Finding Probabilities

Nonstandard Normal Distribution: Finding Scores(Critical Values)

VI. Relations Between Distributions

The Central Limit Theorem

Law of Large Numbers

Normal Distribution as Approximation to Binomial Distribution

Poisson Approximation to Binomial Distribution

Binomial Approximation to Hypergeometric

Normal Approximation to Poisson

VII. Point and Interval Estimates

Method of Moments and Maximum Likelihood Estimation

Estimating a Population Mean: Large Samples

Estimating a Population Mean: Small Samples

Student's T Distribution

Estimating a Population Proportion

Estimating a Population Variance

VIII. Hypothesis Testing

Fundamentals of Hypothesis Testing

Testing a Claim About a Mean: Large Samples

Testing a Claim About a Mean: Small Samples

Testing a Claim About a Proportion

Testing a Claim About a Standard Deviation or Variance

Inferences from Two Samples

IX. Inferences About Two Means: Dependent Samples

Inferences About Two Means: Independent Samples

Comparing Two Variances

Inferences About Two Proportions


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.

Describing 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?

Choose One Answer:

A. Histograms

B. Dot Plots

C. Scatter Plots

D. Box Plots

Measures of Center and 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?

Choose One Answer.

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?

Choose one answer.

A. Mean and interquartile range

B. Mean and standard deviation

C. Median and interquartile range

D. Mean and standard deviation


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%

2. 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 0.30 0.20 0.20 0.1

Choose one answer.

A. 13.5

B. 3.1

C. 2.65

D. 5.2

Statistical Tests

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?

Choose One Answer.

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

Summarizing Data

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. Median and Standard Deviation


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