- 1 Probability and Statistics EBook Practice Problems
- 2 I. Introduction to Statistics
- 3 II. Describing, Exploring, and Comparing Data
- 4 III. Probability
- 5 IV. Probability Distributions
- 6 V. Normal Probability Distribution
- 7 VI. Relations Between Distributions
- 8 VII. Point and Interval Estimates
- 9 VIII. Hypothesis Testing
- 10 Inferences from Two Samples
- 10.1 IX. Inferences About Two Means: Dependent Samples
- 10.2 Inferences About Two Means: Independent Samples
- 10.3 Comparing Two Variances
- 10.4 Inferences About Two Proportions
- 10.5 References
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
Rules for Computing Probabilities
Probabilities Through Simulations
IV. Probability Distributions
Expectation(Mean) and Variance)
Bernoulli and Binomial Experiments
Geometric, Hypergeometric, and Negative Binomial
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.
1. Two random samples were taken to determine backpack load difference between seniors and freshmen, in pounds. The following are the summaries:
Which of the following plots would be the most useful in comparing the two sets of backpack weights?
Choose One Answer:
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:
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.
C. None of the Above
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?
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.
Choose one answer.
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
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
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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