Introductory Statistics
3rd Edition
ISBN: 9780135188927
Author: Gould, Robert, Ryan, Colleen N. (colleen Nooter)
Publisher: Pearson,
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Textbook Question
Chapter 6, Problem 3SE
6.1-6.4 Directions Determine whether each of the following variables would best be modeled as continuous or discrete.
a. The height of a person in inches
b. The weight of a person in pounds
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2. Hypothesis Testing - Two Sample Means
A nutritionist is investigating the effect of two different diet programs, A and B, on weight loss. Two
independent samples of adults were randomly assigned to each diet for 12 weeks. The weight losses (in kg)
are normally distributed.
Sample A: n = 35, 4.8, s = 1.2
Sample B: n=40, 4.3, 8 = 1.0
Questions:
a) State the null and alternative hypotheses to test whether there is a significant difference in mean weight
loss between the two diet programs.
b) Perform a hypothesis test at the 5% significance level and interpret the result.
c) Compute a 95% confidence interval for the difference in means and interpret it.
d) Discuss assumptions of this test and explain how violations of these assumptions could impact the results.
1. Sampling Distribution and the Central Limit Theorem
A company produces batteries with a mean lifetime of 300 hours and a standard deviation of 50 hours. The lifetimes are not normally distributed—they are right-skewed due to some batteries lasting unusually long.
Suppose a quality control analyst selects a random sample of 64 batteries from a large production batch.
Questions:
a) Explain whether the distribution of sample means will be approximately normal. Justify your answer using the Central Limit Theorem.
b) Compute the mean and standard deviation of the sampling distribution of the sample mean.
c) What is the probability that the sample mean lifetime of the 64 batteries exceeds 310 hours?
d) Discuss how the sample size affects the shape and variability of the sampling distribution.
A biologist is investigating the effect of potential plant
hormones by treating 20 stem segments. At the end of
the observation period he computes the following length
averages:
Compound X = 1.18
Compound Y = 1.17
Based on these mean values he concludes that there are
no treatment differences.
1) Are you satisfied with his conclusion? Why or why
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2) If he asked you for help in analyzing these data, what
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why?
3) Are there any other questions you would ask him
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Chapter 6 Solutions
Introductory Statistics
Ch. 6 - Directions Determine whether each of the following...Ch. 6 - 6.1-6.4 Directions Determine whether each of the...Ch. 6 - 6.1-6.4 Directions Determine whether each of the...Ch. 6 - 6.1-6.4 Directions Determine whether each of the...Ch. 6 - Loaded Die (Example 2) A magician has shaved an...Ch. 6 - Prob. 6SECh. 6 - Distribution of Two Thumbtacks When a certain type...Ch. 6 - Two Children Make a list of all possible outcomes...Ch. 6 - Two Thumbtacks a. From your answers in Exercise...Ch. 6 - Two Children Using your list of outcomes in...
Ch. 6 - Snow Depth (Example 3) Eric wants to go skiing...Ch. 6 - Snow Depth Refer to Exercise 6.11. What is the...Ch. 6 - Applying the Empirical Rule with z-Scores The...Ch. 6 - Length of Pregnancy Assume that the lengths of...Ch. 6 - SAT Scores Quantitative SAT scores are...Ch. 6 - Women’s Heights Assume that college women’s...Ch. 6 - Women’s Heights (Example 4) Assume college women’s...Ch. 6 - SAT Scores Quantitative SAT scores are...Ch. 6 - Standard Normal Use the table or technology to...Ch. 6 - Standard Normal Use the table or technology to...Ch. 6 - Standard Normal Use technology or a Normal table...Ch. 6 - Standard Normal Use technology or a Normal table...Ch. 6 - Extreme Positive z -Scores For each question, find...Ch. 6 - Extreme Negative z-Scores For each question, find...Ch. 6 - St. Bernard Dogs (Example 5) According to dogtime...Ch. 6 - Whales Whales have one of the longest gestation...Ch. 6 - Boys’ Foot Length (Example 6) According to the...Ch. 6 - Women’s Foot Length According to the Digital Human...Ch. 6 - Boys’ Foot Length Suppose a shoe store stocks...Ch. 6 - Women’s Foot Length Suppose a shoe store stocks...Ch. 6 - Birth Weights (Example 7) According to the British...Ch. 6 - Birth Lengths According to National Vital...Ch. 6 - White Blood Cells The distribution of white blood...Ch. 6 - Red Blood Cells The distribution of red blood cell...Ch. 6 - SAT Scores in Illinois According to the 2017 SAT...Ch. 6 - SAT Scores in Florida According to the 2017 SAT...Ch. 6 - Arm Span (Men) According to Anthropometric Survey...Ch. 6 - Arm Span (Women) According to Anthropometric...Ch. 6 - New York City Weather New York City’s mean minimum...Ch. 6 - Chicago Weather The average winter daily...Ch. 6 - Probability or Measurement (Inverse)? (Example 8)...Ch. 6 - Probability or Measurement (Inverse)? The Normal...Ch. 6 - Inverse Normal, Standard In a standard Normal...Ch. 6 - Inverse Normal, Standard In a standard Normal...Ch. 6 - Inverse Normal, Standard Assume a standard Normal...Ch. 6 - Inverse Normal, Standard Assume a standard Normal...Ch. 6 - Prob. 47SECh. 6 - Weights of Newborn Hippos The weight of newborn...Ch. 6 - Medical School MCAT Scores on the 2017 MCAT, an...Ch. 6 - Medical School GPA The distribution of grade point...Ch. 6 - Women’s Heights Suppose college women’s heights...Ch. 6 - Men’s Heights Suppose college men’s heights are...Ch. 6 - Inverse SATs Critical reading SAT scores are...Ch. 6 - Inverse Women’s Heights College women have heights...Ch. 6 - Girls’ and Women’s Heights According to the...Ch. 6 - Boys’ and Men’s Heights According to the National...Ch. 6 - Cats’ Birth Weights The average birth weight of...Ch. 6 - Elephants’ Birth Weights The average birth weight...Ch. 6 - Gender of Children (Example 10) A married couple...Ch. 6 - Coin Flip A coin will be flipped four times, and...Ch. 6 - Rolling a Die (Example 11) A die is rolled 5...Ch. 6 - Twins In Exercise 6.59 you are told to assume that...Ch. 6 - Free Throws Professional basketball player...Ch. 6 - On-Time Arrivals Alaska Airlines has an on-time...Ch. 6 - Identifying n,p, and x (Example 12) For each...Ch. 6 - Identifying n,p, and x For each situation,...Ch. 6 - Dog Owners (Example 13) According to the American...Ch. 6 - Cat Owners According to the American Veterinary...Ch. 6 - Passports According to data from the U.S. State...Ch. 6 - Travel According to a survey conducted by OnePoll,...Ch. 6 - Wisconsin Graduation Wisconsin has the highest...Ch. 6 - Colorado Graduation Colorado has a high school...Ch. 6 - Cell Phones According to the Centers of Disease...Ch. 6 - Landlines According to the Centers of Disease...Ch. 6 - Drones (Example 14) The use of drones, aircraft...Ch. 6 - Drones A 2017 Pew Research Center report on drones...Ch. 6 - Texting While Walking According to a report by the...Ch. 6 - Texting While Driving According to a study by the...Ch. 6 - Prob. 79SECh. 6 - Free Throws Professional basketball LeBron James...Ch. 6 - Prob. 81SECh. 6 - Prob. 82SECh. 6 - Discrete or Continuous? Determine whether each of...Ch. 6 - Probability Distribution In a game of chance,...Ch. 6 - Birth Length A study of U.S. births published on...Ch. 6 - Birth Length A study of U.S. births published on...Ch. 6 - Males’ Body Temperatures A study of human body...Ch. 6 - Females’ Body Temperatures A study of human body...Ch. 6 - Prob. 89CRECh. 6 - Medical Licensing See problem 6.89 for information...Ch. 6 - Systolic Blood Pressures Systolic blood pressures...Ch. 6 - Prob. 92CRECh. 6 - Stress According to a 2017 Gallup poll, 44#37; of...Ch. 6 - Stress According to a 2017 Gallup poll, 17 of...Ch. 6 - Voice-Controlled Assistants Voice-controlled video...Ch. 6 - Prob. 96CRECh. 6 - Prob. 97CRECh. 6 - Prob. 98CRECh. 6 - Prob. 99CRECh. 6 - Quantitative SAT Scores, Normal and Binomial The...Ch. 6 - Prob. 101CRECh. 6 - Birth Length and z-Scores, Inverse Babies in the...
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