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Statistics
  • Statistics
  • Chapter 1. Introduction
    • 1-1. Exercises
    • 1-2. Exercises
  • Chapter 2. Descriptive Statistics
    • 2-1. Three Popular Data Displays
    • 2-1. Exercises
    • 2-2. Measures of Central Location (Central Tendency)
    • 2-2. Exercises
    • 2-3. Measures of Variability (Statistical Dispersion)
    • 2-3. Exercises
    • 2-4. Relative Position of Data
    • 2-4. Exercises
    • 2-5. The Empirical Rule and Chebyshev’s Theorem
    • 2-5. Exercises
  • Chapter 3. Basic Concepts of Probability
    • 3-1. Sample Spaces, Events, and Their Probabilities
    • 3-1. Exercises
    • 3-2. Complements, Intersections,and Unions
    • 3-2. Exercises
    • 3-3. Conditional Probability and Independent Events
    • 3-3. Exercises
    • 3-4. Bayes' Theorem
  • Chapter 4. Discrete Random Variables
    • 4-1. Random Variables
    • 4-1. Exercises
    • 4-2. Probability Distributions for Discrete Random Variables
    • 4-2. Exercises
    • 4-3. Uniform Distribution
    • 4-3. Exercises
    • 4-4. Binomial Distribution
    • 4-4. Exercises
    • 4-5. Multinomial Distribution (*)
    • 4-6. Hypergeometric Distribution
    • 4-6. Exercises
    • 4-7. Geometric Distribution
    • 4-8. Negative Binomial Distribution (*)
    • 4-9. Negative Hypergeometric Distribution (*)
    • 4-9. Exercises
    • 4-10. Poisson distribution
    • 4-10. Exercises
  • Chapter 5. Continuous Random Variables
    • 5-1. Continuous Random Variables
    • 5-1. Exercises
    • 5-2. The Standard Normal Distribution
    • 5-2. Exercises
    • 5-3. Probability Computations for General Normal Random Variables
    • 5-3. Exercises
    • 5-4. Areas of Tails of Distributions
    • 5-4. Exercises
    • 5-5. Gamma Distribution (*)
    • 5-6. Exponential Distribution
    • 5-7. Beta Distribution (*)
    • 5-8. Weibull Distribution (*)
  • Chapter 6. Sampling Distributions
    • 6-1. The Mean and Standard Deviation of the Sample Mean
    • 6-1. Exercises
    • 6-2. The Sampling Distribution of the Sample Mean
    • 6-2. Exercises
    • 6-3. The Sample Proportion
    • 6-3. Exercises
  • Chapter 7. Estimation
    • 7-1. Large Sample Estimation of a Population Mean
    • 7-1. Exercises
    • 7-2. Small Sample Estimation of a Population Mean
    • 7-2. Exercises
    • 7-3. Large Sample Estimation of a Population Proportion
    • 7-3. Exercises
    • 7-4. Sample Size Considerations
    • 7-4. Exercises
  • Chapter 8. Testing Hypotheses
    • 8-1. The Elements of Hypothesis Testing
    • 8-1. Exercises
    • 8-2. Large Sample Tests for a Population Mean
    • 8-2. Exercises
    • 8-3. The Observed Significance of a Test
    • 8-3. Exercises
    • 8-4. Small Sample Tests for a Population Mean
    • 8-4. Exercises
    • 8-5. Large Sample Tests for a Population Proportion
    • 8-5. Exercises
  • Chapter 9. Two-Sample Problems
    • 9-1. Comparison of Two Population Means: Large, Independent Samples
    • 9-1. Exercises
    • 9-2. Comparison of Two Population Means: Small, Independent Samples
    • 9-2. Exercises
    • 9-3. Comparison of Two Population Means: Paired Samples
    • 9-3. Exercises
    • 9-4. Comparison of Two Population Proportions
    • 9-4. Exercises
    • 9-5. Sample Size Considerations
    • 9-5. Exercises
  • Chapter 10. Correlation and Regression
    • 10-1. Linear Relationships Between Variables
    • 10-1. Exercises
    • 10-2. The Linear Correlation Coefficient
    • 10-2. Exercises
    • 10-3. Modelling Linear Relationships with Randomness Present
    • 10-3. Exercises
    • 10-4. The Least Squares Regression Line
    • 10-4. Exercises
    • 10-5. Statistical Inferences
    • 10-5. Exercises
    • 10-6. The Coefficient of Determination
    • 10-6. Exercises
    • 10-7. Estimation and Prediction
    • 10-7. Exercises
    • 10-8. A Complete Example
    • 10-8. Exercises
    • 10-9. Formula List
  • Chapter 11. Chi-Square Tests and F-Tests
    • 11-1. Chi-Square Tests for Independence
    • 11-1. Exercises
    • 11-2. Chi-Square One-Sample Goodness-of-Fit Tests
    • 11-2. Exercises
    • 11-3. F-tests for Equality of Two Variances
    • 11-3. Exercises
    • 11-4. F-Tests in One-Way ANOVA
    • 11-4. Exercises
  • Chapter 12. Appendix
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  1. Chapter 8. Testing Hypotheses

8-1. Exercises

Previous8-1. The Elements of Hypothesis TestingNext8-2. Large Sample Tests for a Population Mean

Last updated 5 years ago

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EXERCISES

Ex 1. State the null and alternative hypotheses for each of the following situations. (That is, identify the correct number μ0μ_0μ0​ and write H0:μ=μ0H_0:μ=μ_0H0​:μ=μ0​ and the appropriate analogous expression for HaH_aHa​ .)

  1. The average July temperature in a region historically has been 74.5°F. Perhaps it is higher now.

  2. The average weight of a female airline passenger with luggage was 145 pounds ten years ago. The FAA believes it to be higher now.

  3. The average stipend for doctoral students in a particular discipline at a state university is $14,756. The department chairman believes that the national average is higher.

  4. The average room rate in hotels in a certain region is $82.53. A travel agent believes that the average in a particular resort area is different.

  5. The average farm size in a predominately rural state was 69.4 acres. The secretary of agriculture of that state asserts that it is less today.

Ex 2. State the null and alternative hypotheses for each of the following situations. (That is, identify the correct number μ0μ_0μ0​ and write H0:μ=μ0H_0:μ=μ_0H0​:μ=μ0​ and the appropriate analogous expression for HaH_aHa​.)

  1. The average time workers spent commuting to work in Verona five years ago was 38.2 minutes. The Verona Chamber of Commerce asserts that the average is less now.

  2. The mean salary for all men in a certain profession is $58,291. A special interest group thinks that the mean salary for women in the same profession is different.

  3. The accepted figure for the caffeine content of an 8-ounce cup of coffee is 133 mg. A dietitian believes that the average for coffee served in a local restaurants is higher.

  4. The average yield per acre for all types of corn in a recent year was 161.9 bushels. An economist believes that the average yield per acre is different this year.

  5. An industry association asserts that the average age of all self-described fly fishermen is 42.8 years. A sociologist suspects that it is higher.

Ex 3. Describe the two types of errors that can be made in a test of hypotheses.

Ex 4. Under what circumstance is a test of hypotheses certain to yield a correct decision?