Logout Open In App
Open In App
Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Chapter 10: Q. 84 (page 687)

Explain why it is not appropriate to perform a paired ttest about the true mean difference (Male − Female) in literacy rates in Islamic countries.

Short Answer

Expert verified

All the conditions are not satisfied since the random condition and large sample is not satisfied and it is therefore not appropriate to determine the confidence interval for the population mean difference.

Step by step solution

01

Step 1. To find

Here we have to find why it is not appropriate to perform a paired t test about the true mean difference (Male − Female) in literacy rates in Islamic countries.

02

Step 2. Explanation

To answer the question we must find out if the three conditions are satisfied or not, which is as:

Random: It is not satisfied because the samples included largely Muslim nations and thus the small nations were ignored which implies no random sample.

Independent: It is satisfied because the sample of Muslim nations is less than of all population of Muslim nations.

Normal: It is not satisfied because the sample is not large and the distribution is not approximately Normal.

Thus, all the conditions are not satisfied since the random condition and large sample is not satisfied and it is therefore not appropriate to determine the confidence interval for the population mean difference.

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

The distribution of grade point averages (GPAs) for a certain college is approximately Normal with a mean of 2.5 and a standard deviation of 0.6. The minimum possible GPA is 0.0 and the maximum possible GPA is 4.33. Any student with a GPA less than 1.0 is put on probation, while any student with a GPA of 3.5 or higher is on the dean’s list. About what percent of students at the college are on probation or on the dean’s list?

a.0.6b.4.7c.5.4d.94.6e.95.3

Shrubs and fire Fire is a serious threat to shrubs in dry climates. Some shrubs can

resprout from their roots after their tops are destroyed. Researchers wondered if fire would help with resprouting. One study of resprouting took place in a dry area of Mexico. The researchers randomly assigned shrubs to treatment and control groups. They clipped the tops of all the shrubs. They then applied a propane torch to the stumps of the treatment group to simulate a fire. All 12of the shrubs in the treatment group resprouted. Only 8of the 12shrubs in the control group resprouted.

a. State appropriate hypotheses for performing a significance test. Be sure to define the parameters of interest.

b. Check if the conditions for performing the test are met.

Each day I am getting better in math A "subliminal" message is below our threshold of awareness but may nonetheless influence us. Can subliminal messages help students learn math? A group of 18students who had failed the mathematics part of the City University of New York Skills Assessment Test agreed to participate in a study to find out. All received a daily subliminal message, flashed on a screen too rapidly to be consciously read. The treatment group of 10students (assigned at random) was exposed to "Each day I am getting better in math." The control group of 8students was exposed to a neutral message, "People are walking on the street." All 18students participated in a summer program designed to improve their math skills, and all took the assessment test again at the end of the program. The following table gives data on the subjects' scores before and after the program.

a. Explain why a two-sample t-test and not a paired t-test is the appropriate inference procedure in this setting.

b. The following boxplots display the differences in pretest and post-test scores for the students in the control (C) and treatment (T) groups. Write a few sentences comparing the performance of these two groups.

c. Do the data provide convincing evidence at the α=0.01,3051526=0.200=20%significance level that subliminal messages help students like the ones in this study learn math, on average?

d. Can we generalize these results to the population of all students who failed the mathematics part of the City University of New York Skills Assessment Test? Why or why not?

Researchers suspect that Variety A tomato plants have a different average yield than Variety B tomato plants. To find out, researchers randomly select10Variety A and10Variety B tomato plants. Then the researchers divide in half each of10small plots of land in different locations. For each plot, a coin toss determines which half of the plot gets a Variety A plant; a Variety B plant goes in the other half. After harvest, they compare the yield in pounds for the plants at each location. The10differences (Variety A − Variety B) in yield are recorded. A graph of the differences looks roughly symmetric and single-peaked with no outliers. The mean difference is x-=0.343051526=0.200=20%x-A-B=0.34and the standard deviation of the differences is s A-B=0.833051526=0.200=20%=sA-B=0.83.LetμA-B=3051526=0.200=20%μA−B = the true mean difference (Variety A − Variety B) in yield for tomato plants of these two varieties.

The P-value for a test of H0: μA−B=03051526=0.200=20%versus Ha: μA−B≠0 is 0.227. Which of the following is the

correct interpretation of this P-value?

a. The probability that μA−B is0.227.

b. Given that the true mean difference (Variety A – Variety B) in yield for these two varieties of tomato plants is0, the probability of getting a sample mean difference of0.34is0.227.

c. Given that the true mean difference (Variety A – Variety B) in yield for these two varieties of tomato plants is0, the probability of getting a sample mean difference of0.34or greater is0.227.

d. Given that the true mean difference (Variety A – Variety B) in yield for these two varieties of tomato plants is0, the probability of getting a sample mean difference greater than or equal to0.34or less than or equal to −0.34is0.227.

e. Given that the true mean difference (Variety A – Variety B) in yield for these two varieties of tomato plants is not 0, the probability of getting a sample mean difference greater than or equal to 0.34or less than or equal to −0.34is0.227.

According to sleep researchers, if you are between the ages of 12and 18years old, you need 9 hours of sleep to function well. A simple random sample of 28students was chosen from a large high school, and these students were asked how much sleep they got the previous night. The mean of the responses was 7.9hours with a standard deviation of 2.1hours.

Which of the following is the standardized test statistic for the hypothesis test ?

  1. localid="1654221307488" t=7.9-92.128andt=7.9-92.128
  2. t=9-7.92.128andt=9-7.92.128
  3. t=7.9-92.128and t=7.9-92.128
  4. localid="1654221494579" t=7.9-92.127andt=7.9-92.127
  5. localid="1654221497857" t=9-7.92.127andt=9-7.92.127
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Discrete 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