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

Videos

Textbook Question
Book Icon
Chapter 10, Problem 72CP

Pick the method Steve Solomon, the owner of Leonardo’s Italian restaurant, wonders whether a redesigned menu will increase, on the average, the amount that customers spend in the restaurant. For the following scenarios, pick a statistical method from this chapter that would be appropriate for analyzing the data, indicating whether the samples are independent or dependent, which parameter is relevant, and what inference method you would use:

  1. a. Solomon records the mean sales the week before the change and the week after the change and then wonders whether the difference is “statistically significant.”
  2. b. Solomon randomly samples 100 people and shows them each both menus, asking them to give a rating between 0 and 10 for each menu.
  3. c. Solomon randomly samples 100 people and shows them each both menus, asking them to give an overall rating of positive or negative to each menu.
  4. d. Solomon randomly samples 100 people and randomly separates them into two groups of 50 each. He asks those in Group 1 to give a rating to the old menu and those in Group 2 to give a rating to the new menu, using a 0 to 10 rating scale.

a.

Expert Solution
Check Mark
To determine

Pick a statistical method that is appropriate for analyzing the data.

Indicate whether samples are independent or dependent.

Indicate the relevant parameter.

Find the inference method that can be used.

Explanation of Solution

It is given that Person S records the mean sales before and after the change and wanted to check whether the difference is statistically significant.

Statistical method:

This is a significance test as Solomon wanted to check whether the difference is “statistically significant”.

Independent or dependent:

The observations of mean sales in the week before the change are independent with the mean sales in the week after the change. Therefore, the samples are independent.

Relevant parameter:

In order to test whether the difference is significant based on mean sales, the relevant parameter is the mean difference between mean sales.

Inference method:

This scenario refers to the significance test for comparing population means. Thus, the appropriate test can perform using t-statistic and P-value. The null hypothesis is rejected, if P-value is less than or equal to significance level.

b.

Expert Solution
Check Mark
To determine

Choose a statistical method that is appropriate for analyzing the data.

Explain whether samples are independent or dependent.

Find the relevant parameter.

Obtain the inference method that can be used.

Explanation of Solution

It is given that Person S randomly samples 100 people and shows them both menus. For each menu, sample is asked to rate between 0 and 10.

Statistical method:

The statistical method is either confidence interval method or significance test.

Independent or dependent:

Since the both menus were showed to same 100 people (that is, two samples involving same subjects), the samples are dependent.

Relevant parameter:

The relevant parameter is the mean difference score of 100 people between two scores of menus.

Inference method:

If statistical method of confidence interval satisfies, then confidence interval calculation would be the inference method for this scenario. Otherwise, t-statistic and P-value method of significance test for comparing population means would be the inference method.

c.

Expert Solution
Check Mark
To determine

Select a statistical method that is appropriate for analyzing the data.

Choose whether samples are independent or dependent.

Explain about the relevant parameter.

Prefer the inference method that can be used.

Explanation of Solution

It is given that Person S randomly samples 100 people and shows them both menus. The sample is asked for overall rating (positive or negative) to each menu.

Statistical method:

Overall rating of positive or negative refers to the comparison of proportions. Thus, the method for comparing proportions for dependent sample is either McNemar test of significance or confidence interval (if the confidence interval contains 0).

Independent or dependent:

Since the both menus were showed to same 100 people (that is, two samples involving same subjects), the samples are dependent.

Relevant parameter:

The relevant parameter is the difference between proportions between two scores of menus.

Inference method:

If statistical method of confidence interval satisfies, then confidence interval calculation would be the inference method for this scenario. Otherwise, to compare two proportions

with dependent data, z-score and P-value method using McNemar test would be the inference method.

d.

Expert Solution
Check Mark
To determine

State a statistical method that is appropriate for analyzing the data.

Check whether samples are independent or dependent.

Find the relevant parameter.

Obtain the inference method that can be used.

Explanation of Solution

It is given that Person S randomly samples 100 people and randomly separates them into two groups of 50 each. Then, using a 0 to 10 rating scale, group 1 was asked to rate the old menu and group 2 was asked to rate new menu.

Statistical method:

The statistical method is either confidence interval method or significance test.

Independent or dependent:

Since the observations in group 1 and group 2 are not same, (that is, two samples involving different subjects), the samples are independent.

Relevant parameter:

The relevant parameter is the mean difference score between group 1 and group 2.

Inference method:

If statistical method of confidence interval satisfies, then confidence interval calculation would be the inference method for this scenario. Otherwise, t-statistic and P-value method for significance test for comparing population means would be the inference method.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Chapter 10 Solutions

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

Ch. 10.1 - Hormone therapy for menopause The Womens Health...Ch. 10.1 - Obama A/B testing To increase Barack Obamas...Ch. 10.1 - Believe in heaven and hell A recent survey asked...Ch. 10.2 - Alcohol and Energy Drinks A 2013 article in the...Ch. 10.2 - Address global warming You would like to determine...Ch. 10.2 - Housework for women and men Do women tend to spend...Ch. 10.2 - More confident about housework Refer to part c in...Ch. 10.2 - Employment by gender The study described in...Ch. 10.2 - Ideal number of children In 2014, the GSS asked,...Ch. 10.2 - Pay by gender The study described in the Exercise...Ch. 10.2 - Bulimia CI A study of bulimia among college women...Ch. 10.2 - Chelation useless? Chelation is an alternative...Ch. 10.2 - Nicotine dependence A study on nicotine dependence...Ch. 10.2 - Inhaling affect HONC? Refer to the previous...Ch. 10.2 - Females or males more nicotine dependent? Refer to...Ch. 10.2 - Female and male monthly smokers Refer to the...Ch. 10.2 - Body language In an experiment investigating body...Ch. 10.2 - Student survey Refer to the FL Student Survey data...Ch. 10.2 - Study time A graduate teaching assistant for...Ch. 10.2 - More on study time Refer to the data in the...Ch. 10.2 - Time spent on social networks As part of a class...Ch. 10.2 - More time on social networks In the previous...Ch. 10.2 - Normal assumption The methods of this section make...Ch. 10.2 - Vital capacity One of the authors of this book has...Ch. 10.3 - Body dissatisfaction Female college student...Ch. 10.3 - Body dissatisfaction test Refer to the previous...Ch. 10.3 - Surgery versus placebo for knee pain Refer to...Ch. 10.3 - Comparing clinical therapies A clinical...Ch. 10.3 - Clinical therapies 2 Refer to the previous...Ch. 10.3 - Vegetarians more liberal? When a sample of social...Ch. 10.3 - Teeth whitening results One scientific test of...Ch. 10.3 - Permuting therapies Refer to Exercise 10.38, which...Ch. 10.3 - Permutations equally likely Refer to the previous...Ch. 10.3 - Two-sided permutation P-value Refer to the...Ch. 10.3 - Time spent on social networks revisited Exercise...Ch. 10.3 - Compare permutation test to t test Refer to the...Ch. 10.3 - Dominance of politicians For a rating experiment,...Ch. 10.3 - Sampling distribution of x1x2 Refer to Example 12,...Ch. 10.4 - Does exercise help blood pressure? Several recent...Ch. 10.4 - Test for blood pressure Refer to the previous...Ch. 10.4 - Social activities for students As part of her...Ch. 10.4 - More social activities Refer to the previous...Ch. 10.4 - Movies versus parties Refer to the previous two...Ch. 10.4 - Freshman 15 a myth? The freshman 15 is the name of...Ch. 10.4 - Checking for freshman 15 Refer to the previous...Ch. 10.4 - Internet book prices Annas project for her...Ch. 10.4 - Comparing hook prices 2 For the data in the...Ch. 10.4 - Lung capacity revisited Refer to Exercise 10.34...Ch. 10.4 - Comparing speech recognition systems Table 1020 in...Ch. 10.4 - Treat juveniles as adults? The table that follows...Ch. 10.4 - Change coffee brand? A study was conducted to see...Ch. 10.4 - Presidents popularity Last month a random sample...Ch. 10.4 - Heaven and hell Results of polls about belief in...Ch. 10.4 - Heaven and hell around the world Refer to the...Ch. 10.5 - Prob. 65PBCh. 10.5 - Prob. 66PBCh. 10.5 - Basketball paradox The following list summarizes...Ch. 10.5 - Prob. 68PBCh. 10.5 - Prob. 69PBCh. 10.5 - Prob. 70PBCh. 10.5 - Breast cancer over time The percentage of women...Ch. 10 - Pick the method Steve Solomon, the owner of...Ch. 10 - Prob. 73CPCh. 10 - BMI then and now The Centers for Disease Control...Ch. 10 - Marijuana and gender In a survey conducted by...Ch. 10 - Prob. 76CPCh. 10 - Belief depend on gender? Refer to the previous...Ch. 10 - Prob. 78CPCh. 10 - Prob. 79CPCh. 10 - Prob. 80CPCh. 10 - Prob. 81CPCh. 10 - Prob. 82CPCh. 10 - Prob. 83CPCh. 10 - Prob. 84CPCh. 10 - Prob. 85CPCh. 10 - How often do you feel sad? A recent General Social...Ch. 10 - Prob. 87CPCh. 10 - Prob. 88CPCh. 10 - Prob. 89CPCh. 10 - Equal pay in sports? The following data refer to a...Ch. 10 - Prob. 91CPCh. 10 - Prob. 92CPCh. 10 - Anorexia again Refer to Exercise 10.89, comparing...Ch. 10 - Breast-feeding helps IQ? A Danish study of...Ch. 10 - Prob. 95CPCh. 10 - Prob. 96CPCh. 10 - Prob. 97CPCh. 10 - Prob. 98CPCh. 10 - Prob. 99CPCh. 10 - Prob. 100CPCh. 10 - Prob. 101CPCh. 10 - Prob. 102CPCh. 10 - Prob. 103CPCh. 10 - Prob. 104CPCh. 10 - Belief in ghosts and in astrology A poll by Louis...Ch. 10 - Death penalty paradox Exercise 3.58 showed results...Ch. 10 - Prob. 107CPCh. 10 - Prob. 108CPCh. 10 - Prob. 109CPCh. 10 - Prob. 111CPCh. 10 - Pay discrimination against women? A Time Magazine...Ch. 10 - Mean of permutation distribution Refer to Example...Ch. 10 - Treating math anxiety Two new programs were...Ch. 10 - Prob. 115CPCh. 10 - Prob. 116CPCh. 10 - Prob. 117CPCh. 10 - Multiple choice: Sample size and significance If...Ch. 10 - Prob. 119CPCh. 10 - Prob. 120CPCh. 10 - Prob. 121CPCh. 10 - Prob. 122CPCh. 10 - Prob. 123CPCh. 10 - Prob. 124CPCh. 10 - Prob. 125CPCh. 10 - Prob. 126CPCh. 10 - Null standard error for matched pairs Under the...Ch. 10 - Prob. 128CP
Knowledge Booster
Background pattern image
Statistics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Text book image
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Text book image
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
Text book image
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Hypothesis Testing using Confidence Interval Approach; Author: BUM2413 Applied Statistics UMP;https://www.youtube.com/watch?v=Hq1l3e9pLyY;License: Standard YouTube License, CC-BY
Hypothesis Testing - Difference of Two Means - Student's -Distribution & Normal Distribution; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=UcZwyzwWU7o;License: Standard Youtube License