Statistics: The Art and Science of Learning from Data (4th Edition)

4th Edition

ISBN: 9780321997838

Author: Alan Agresti, Christine A. Franklin, Bernhard Klingenberg

Publisher: PEARSON

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Textbook Question

Chapter 9.3, Problem 31PB

Low carbohydrate diet In a recent study,⁸ 272 moderately obese subjects were randomly assigned to one of three diets: low-fat, restricted-calorie; Mediterranean, restricted-calorie; or low-carbohydrate, nonrestricted-calorie. The prediction was that subjects on a low-carbohydrate diet would lose weight, on the average. After two years, the mean weight loss was 5.5 kg for the 109 subjects in the low-carbohydrate group with a standard deviation of 7.0 kg. The MINITAB output shows results of a significance test for testing H₀: µ = 0 against H_a: µ ≠ 0, where m is the population mean weight change. Note that weight change is determined by calculating after weight — before weight.

Chapter 9.3, Problem 31PB, Low carbohydrate diet In a recent study,8 272 moderately obese subjects were randomly assigned to

a. Identify the P-value for this test.
b. How is the P-value interpreted?
c. Would the P-value and 95% confidence interval lead to
d. the same conclusion about H₀? Explain.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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Chapter 9.3, Problem 30PB

Chapter 9.3, Problem 32PB

Chapter 9 Solutions

Statistics: The Art and Science of Learning from Data (4th Edition)

Ch. 9.1 - H0 or Ha? For parts a and b, is the statement a...Ch. 9.1 - H0 or Ha? For each of the following, is the...Ch. 9.1 - Burden of proof For a new pesticide, should the...Ch. 9.1 - Financial aid The average financial aid package...Ch. 9.1 - Low-carbohydrate diet A study plans to have a...Ch. 9.1 - Prob. 6PB Ch. 9.1 - Proper hypotheses? Explain what is wrong with each...Ch. 9.1 - Prob. 8PB Ch. 9.1 - P-value Indicate whether each of the following...Ch. 9.2 - Psychic A person who claims to be psychic says he...

Ch. 9.2 - Prob. 11PB Ch. 9.2 - Get P-value from z For a test of H0: p = 0.50, the...Ch. 9.2 - Get more P-values from z Refer to the previous...Ch. 9.2 - Find test statistic and P-value For a test of H0:...Ch. 9.2 - Dogs and cancer A recent study4 considered whether...Ch. 9.2 - Religion important in your life? Americans ages 18...Ch. 9.2 - Prob. 17PB Ch. 9.2 - Prob. 18PB Ch. 9.2 - Testing a headache remedy Studies that compare...Ch. 9.2 - Gender bias in selecting managers For a large...Ch. 9.2 - Gender discrimination Refer to the 95% confidence...Ch. 9.2 - Garlic to repel ticks A study (J. Amer. Med....Ch. 9.2 - Exit-poll predictions According to an exit poll of...Ch. 9.2 - Which cola? The 49 students in a class at the...Ch. 9.2 - How to sell a burger A fast-food chain wants to...Ch. 9.2 - A binomial headache A null hypothesis states that...Ch. 9.2 - P-value for small samples Example 4, on whether...Ch. 9.3 - Which t has P-value = 0.05? A t test for a mean...Ch. 9.3 - Practice mechanics of a t test A study has a...Ch. 9.3 - Prob. 30PB Ch. 9.3 - Low carbohydrate diet In a recent study,8 272...Ch. 9.3 - Prob. 32PB Ch. 9.3 - Facebook friends Many students brag that they have...Ch. 9.3 - Lake pollution An industrial plant claims to...Ch. 9.3 - Weight change for controls A disadvantage of the...Ch. 9.3 - Crossover study A crossover study of 13 children...Ch. 9.3 - Too little or too much wine? Wine-pouring vending...Ch. 9.3 - Prob. 38PB Ch. 9.3 - Assumptions important? Refer to the previous...Ch. 9.3 - Anorexia in teenage girls Example 8 described a...Ch. 9.3 - Sensitivity study Ideally, results of a...Ch. 9.3 - Prob. 42PB Ch. 9.4 - Dr. Dog In the experiment in Example 4, we got a...Ch. 9.4 - Error probability A significance test about a...Ch. 9.4 - Fracking errors Example 6, in testing H0: p = 0.5...Ch. 9.4 - Prob. 46PB Ch. 9.4 - Anorexia decision Refer to the previous exercise....Ch. 9.4 - Prob. 48PB Ch. 9.4 - Errors in medicine Consider the test of H0: The...Ch. 9.4 - Prob. 50PB Ch. 9.4 - Detecting prostate cancer Refer to the previous...Ch. 9.4 - Prob. 52PB Ch. 9.5 - Misleading summaries? Two researchers conduct...Ch. 9.5 - Practical significance A study considers whether...Ch. 9.5 - Prob. 55PB Ch. 9.5 - Fishing for significance A marketing study...Ch. 9.5 - Prob. 57PB Ch. 9.5 - Prob. 58PB Ch. 9.5 - Interpret medical research studies a. An...Ch. 9.6 - Find P(Type II error) A study is designed to test...Ch. 9.6 - Gender bias in selecting managers Exercise 9.20...Ch. 9.6 - Prob. 62PB Ch. 9.6 - P(Type II error) large when p close to H0 For...Ch. 9.6 - Prob. 64PB Ch. 9.6 - Power for infertility trial Consider Example 13...Ch. 9.6 - Exploring Type II errors Refer to the web app from...Ch. 9 - H0 or Ha? For each of the following hypotheses,...Ch. 9 - Write H0 and Ha For each of the following...Ch. 9 - Prob. 69CP Ch. 9 - Free-throw accuracy Consider all cases in which a...Ch. 9 - Brown or Whitman? Californias governor election in...Ch. 9 - Prob. 72CP Ch. 9 - Prob. 73CP Ch. 9 - Prob. 74CP Ch. 9 - Prob. 75CP Ch. 9 - Start a hockey team A fraternity at a university...Ch. 9 - Prob. 77CP Ch. 9 - Prob. 78CP Ch. 9 - Prob. 79CP Ch. 9 - Prob. 80CP Ch. 9 - Prob. 81CP Ch. 9 - Two ideal children? Is the ideal number of...Ch. 9 - Prob. 83CP Ch. 9 - Prob. 84CP Ch. 9 - Blood pressure When Vincenzo Baranellos blood...Ch. 9 - Increasing blood pressure In the previous...Ch. 9 - Tennis balls in control? When it is operating...Ch. 9 - Prob. 88CP Ch. 9 - Prob. 89CP Ch. 9 - CI and test Refer to the previous exercise. a. For...Ch. 9 - Prob. 91CP Ch. 9 - Religious beliefs statistically significant? A...Ch. 9 - Prob. 93CP Ch. 9 - Prob. 94CP Ch. 9 - Prob. 95CP Ch. 9 - Prob. 96CP Ch. 9 - Prob. 98CP Ch. 9 - Baseball home team advantage In Major League...Ch. 9 - Prob. 100CP Ch. 9 - Prob. 101CP Ch. 9 - Prob. 102CP Ch. 9 - Prob. 103CP Ch. 9 - Prob. 104CP Ch. 9 - Prob. 105CP Ch. 9 - Prob. 106CP Ch. 9 - Prob. 107CP Ch. 9 - Prob. 108CP Ch. 9 - Significance Explain the difference between...Ch. 9 - More doctors recommend An advertisement by Company...Ch. 9 - Prob. 111CP Ch. 9 - Bad P-value interpretations A random sample of...Ch. 9 - Prob. 113CP Ch. 9 - Prob. 114CP Ch. 9 - Prob. 115CP Ch. 9 - Prob. 116CP Ch. 9 - Prob. 117CP Ch. 9 - Prob. 118CP Ch. 9 - Prob. 119CP Ch. 9 - Prob. 120CP Ch. 9 - Prob. 121CP Ch. 9 - True or false A 95% confidence interval for =...Ch. 9 - Prob. 123CP Ch. 9 - Prob. 124CP Ch. 9 - Prob. 125CP Ch. 9 - Prob. 126CP Ch. 9 - Prob. 127CP Ch. 9 - Prob. 128CP

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Solution Summary: The author analyzes the P-value and 95% confidence interval for the null hypothesis H_0.

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