Consider the results of the study discussed on page 417. At α = 0.05, can you support the claim that there is a difference between the proportion of yoga users who are 40- to 49-year-olds and the proportion of non-yoga users who are 40- to 49-year-olds?
Answer: Page A37
In Chapter 6, you were introduced to
Using data from the National Health Interview Survey, a study was conducted to analyze the characteristics of yoga users and non-yoga users. The study was published in the Journal of General Internal Medicine. Some of the results are shown below for a random sample of yoga users.
Yoga Users (n = 1593) | ||
Characteristic | Frequency | Proportion |
40 to 49 years old | 367 | 0,2304 |
Income of $20,000 to S34,999 | 239 | 0,1500 |
Non-smoking | 1323 | 0,8305 |
In this chapter, you will continue your study of inferential statistics and hypothesis testing. Now, however, instead of testing a hypothesis about a single population, you will learn how to test a hypothesis that compares two populations.
For instance, in the yoga study, a random sample of non-yoga users was also surveyed. Here are the study’s findings for this second group.
Non-Yoga Users (n = 29,948) | ||
Characteristic | Frequency | Proportion |
40 to 49 years old | 6,290 | 0,2100 |
Income of $20,000 to $34,999 | 5,990 | 0,2000 |
Non-smoking | 23,360 | 0,7800 |
From these two samples, can you conclude that there is a difference in the proportion of 40- to 49-year-olds, people with an income of $20,000 to $34,999, or non-smokers between yoga users and non-yoga users? Or, might the differences in the proportions be due to chance?
In this chapter, you will learn to answer these questions by testing the hypothesis that the two proportions are equal. For instance, for non-smokers, you can conclude that the proportion of yoga users is different from the proportion of non-yoga users.
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Chapter 8 Solutions
MYLAB STATISTICS: ELEMENTARY STATISTICS
- Suppose that you take a sample of 100 from a population that contains 45 percent Democrats. What sample size condition do you need to check here (if any)?What’s the standard error of ^P?Compare the standard errors of ^p n=100 for ,n=1000 , n=10,000, and comment.arrow_forwardSuppose that a class’s test scores have a mean of 80 and standard deviation of 5. You choose 25 students from the class. What’s the chance that the group’s average test score is more than 82?arrow_forwardSuppose that you collect data on 10 products and check their weights. The average should be 10 ounces, but your sample mean is 9 ounces with standard deviation 2 ounces. Find the standard score.What percentile is the standard score found in part a of this question closest to?Suppose that the mean really is 10 ounces. Do you find these results unusual? Use probabilities to explain.arrow_forward
- Suppose that you want to sample expensive computer chips, but you can have only n=3 of them. Should you continue the experiment?arrow_forwardSuppose that studies claim that 40 percent of cellphone owners use their phones in the car while driving. What’s the chance that more than 425 out of a random sample of 1,000 cellphone owners say they use their phones while driving?arrow_forwardSuppose that the average length of stay in Europe for American tourists is 17 days, with standard deviation 4.5. You choose a random sample of 16 American tourists. The sample of 16 stay an average of 18.5 days or more. What’s the chance of that happening?arrow_forward
- How do you recognize that a statistical problem requires you to use the CLT? Think of one or two clues you can look for. (Assume quantitative data.)arrow_forwardSuppose that you take a sample of 100 from a skewed population with mean 50 and standard deviation 15. What sample size condition do you need to check here (if any)?What’s the shape and center of the sampling distribution for ?What’s the standard error?arrow_forwardQuestion 3 The following stem-and-leaf displays the weekly salary of employees at this firm. Stem-and-Leaf Display Leaf Unit = 10.0 N=x 5 3 00123 12 4 0125888 (y) 5 11234456777 z 6 13568 5 7 154 2 8 46 i. Determine the value of x, y and z. [3] ii. What is the value of the median? [2] iii. Find the mode of this data set. iv. Calculate the range [1] [2]arrow_forward
- Let Y be a continuous RV with PDF otherwise Find the CDF, Fry), of Y . Find an expression for pth, p € (0, 1), quantile of the distribution. Find E(Y) and V(Y). Find E(-2Y + 1) and V(-3Y - 2). Find E(Y3).arrow_forwardLet X be a continuous RV with CDF Find P(X < 0), P(-1 < X < 1) and P(0.5 < X). Based on your answers to the above questions, what is the median of the distribu-tion? Why Find the PDF, fx (x), of X.arrow_forwardA survey of 581 citizens found that 313 of them favor a new bill introduced by the city. We want to find a 95% confidence interval for the true proportion of the population who favor the bill. What is the lower limit of the interval? Enter the result as a decimal rounded to 3 decimal digits. Your Answer:arrow_forward
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