Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 10: Q.31 (page 671)

A researcher wants to determine whether or not a five-week crash diet is effective over a long period of time. A random sample of 15 dieters is selected. Each person’s weight is recorded before starting the diet and one year after it is concluded. Based on the data shown below (weight in pounds), can we conclude that the diet has a long-term effect, that is, that dieters managed to not regain the weight they lost? Include appropriate statistical evidence to justify your answer.

Short Answer

Expert verified

Critical value of t at 0.05level of significance =1.76131

As t<1.76131, we do not reject the null hypothesis and conclude that the five -week crash diet is not effective over a long period of time.

Step by step solution

01

Step 1. given information

We have given the weight of the person before diet and after diet in pounds.

02

Step 2. Simplify

The null and alternative hypothesis is given by :

H0:μd=0H1:μd>0

Where is the mean of the deviation.

The test static is given by,

t=dSd(d)~tn-1

Where d is the mean of deviation in the paired sample.

We have to reject the null hypothesis ift>tα,n-1

now,

And,

The above table is obtained from excel.

The value of test static t=0.312361

Critical value of t at 0.05level of significance =1.76131

As t<1.76131,we do not reject the null hypothesis and conclude that the five -week crash diet is not effective over a long period of time.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Paired or unpaired? In each of the following settings, decide whether you should use paired t procedures or two-sample t procedures to perform inference. Explain your choice. +3

(a) To compare the average weight gain of pigs fed two different rations, nine pairs of pigs were used. The pigs in each pair were littermates. A coin toss was used to decide which page in each pair got Ration and which got Ration B.

(b) A random sample of college professors is taken.

We wish to compare the average salaries of male and female teachers.

(c) To test the effects of a new fertilizer, plots are treated with the new fertilizer, and plots are treated with another fertilizer. A computer's random number generator is used to determine which plots get which fertilizer.

Quality control (2.2,5.3,6.3)Many manufacturing companies use statistical techniques to ensure that the products they make meet standards. One common way to do this is to take a random sample of products at regular intervals throughout the production shift. Assuming that the process is working properly, the mean measurements from these random samples will vary Normally around the target mean μ, with a standard deviation of σ. For each question that follows, assume that the process is working properly.

(a) What's the probability that at least one of the next two sample means will fall more than 2σfrom the target mean μ? Show your work.

(b) What's the probability that the first sample mean that is greater than μ+2σis the one from the fourth sample taken?

(c) Plant managers are trying to develop a criterion for determining when the process is not working properly. One idea they have is to look at the 5 most recent sample means. If at least 4of the 5 fall outside the interval(μ-σ,μ+σ), they will conclude that the process isn't working. Is this a reasonable criterion? Justify your answer with an appropriate probability.

The two-sample t statistic for the road rage study (male mean minus female mean) is t=3.18. The P-value for testing the hypotheses from the previous exercise satisfies

(a) 0.001<P<0.005.

(b) 0.0005<P<0.001.

(c) 0.001<P<0.002.

(d) 0.002<P<0.01.

(e) P>0.01.

40. Household size How do the numbers of people living in households in the United Kingdom (U.K.) and South Africa compare? To help answer this question, we used Census At School’s random data selector to choose independent samples of 50 students from each country. Here is a Fathom dotplot of the household sizes reported by the students in the survey.

Which of the following is false?

(a) A measure of center alone does not completely describe the characteristics of a set of data. Some measure of spread is also needed.

(b) If the original measurements are expressed in inches, the standard deviation would be expressed in square inches.

(c) One of the disadvantages of a histogram is that it doesn’t show each data value.

(d) Between the range and the interquartile range, the IQR is a better measure of spread if there are outliers.

(e) If a distribution is skewed, the median and interquartile range should be reported rather than the mean and standard deviation.
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free