Computer gaming Do experienced computer game players earn higher scores when they play with someone present to cheer them on or when they play alone? Fifty teenagers who are experienced at playing a particular computer game have volunteered for a study . We randomly assign 25of them to play the game alone and the other 25to play the game with a supporter present. Each player’s score is recorded.

(a) Is this a problem with comparing means or comparing proportions? Explain.

(b) What type of study design is being used to produce data?

Short Answer

Expert verified

From the given information,

a) This is a problem with comparing means.

b) Experiment type of study design is being used to produce data

Step by step solution

01

Part (a) Step 1: Given Information

It is given in the question that, Fifty teenagers who are experienced at playing a particular computer game have volunteered for a study. We randomly assign 25of them to play the game alone and the other 25to play the game with a supporter present. Each player’s score is recorded

02

Part (a) Step 2: Explanation

A total of 50youngsters were chosen for a study to see if they earn more when they are cheered up or when they play alone. They were separated into two groups.

The scores of the players are being noted in this scenario, and scores are considered to be quantitative values. The average score gained by each player might be calculated using this information and used to make comparisons. As a result, it's possible to conclude that the issue is one of proportion.

03

Part (b) Step 3: Given Information

It is given in the question, What type of study design is being used to produce data?

04

Part (b) Step 4: Explanation

An experimental study is a study in which the condition is controlled by an operator or researcher. In this scenario, the supporters were purposefully assigned to see how it affected the player's score.

As a result, the given research is an experiment.

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.

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

Coaching and SAT scores (10.1) What proportion of students who take the SAT twice are coached? To answer this question, Jannie decides to construct a 99%confidence interval. Her work is shown below. Explain what’s wrong with Jannie’s method.

A 99%CI for p1-p2is

(0.135-0.865)±2.5750.135(0.865)3160+0.865(0.135)2733=-0.73±0.022=(-0.752,-0.708)

We are 99% confident that the proportion of students taking the SAT twice who are coached is between 71 and 75 percentage points lower than students who aren’t coached.

A large toy company introduces a lot of new toys to its product line each year. The company wants to predict the demand as measured by y, first-year sales (in millions of dollars) using x, awareness of the product (as measured by the proportion of customers who had heard of the product by the end of the second month after its introduction). A random sample of 65new products was taken, and a correlation of 0.96was computed. Which of the following is a correct interpretation of this value?

(a) Ninety-six percent of the time, the least-squares regression line accurately predicts first-year sales.

(b) About 92%of the time, the proportion of people who have heard of the product by the end of the second month will correctly predict first-year sales.

(c) About 92%of first-year sales can be explained by the proportion of people who have heard of the product by the end of the second month.

(d) The least-squares regression line relating the proportion of people who have heard of the product by the end of the second month and first-year sales will have a slope of 0.96.

(e) Ninety-two percent of the variation in first-year sales can be explained by the least-squares regression line with proportion of people who have heard of the product by the end of the second month as the explanatory variable.

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.

“Would you marry a person from a lower social class than your own?” Researchers asked this question of a random sample of 385black, never married students at two historically black colleges in the South. Of the 149men in the sample, 91said “Yes.” Among the 236women, 117said “Yes.”14Is there reason to think that different proportions of men and women in this student population would be willing to marry beneath their class?

Holly carried out the significance test shown below to answer this question. Unfortunately, she made some mistakes along the way. Identify as many mistakes as you can, and tell how to correct each one.

State: I want to perform a test of

H0:p1=p2

Ha:p1p2

at the 95%confidence level.

Plan: If conditions are met, I’ll do a one-sample ztest for comparing two proportions.

  • Random The data came from a random sample of 385 black, never-married students.
  • Normal One student’s answer to the question should have no relationship to another student’s answer.
  • Independent The counts of successes and failures in the two groups91,58,117, and 119are all at least 10

Do: From the data, p^1=91149=0.61and p^2=117236=0.46.

Test statistic

z=(0.61-0.46)-00.61(0.39)149+0.46(0.54)236=2.91

p=value From Table A, role="math" localid="1650292307192" P(z2.91)1-0.39820.0018.

Conclude: The p-value, 0.0018, is less than 0.05, so I’ll reject the null hypothesis. This proves that a higher proportion of men than women are willing to marry someone from a social class lower than their own.

A large clinical trial of the effect of diet on breast cancer assigned women at random to either a normal diet or a low-fat diet. To check that the random assignment did produce comparable groups, we can compare the two groups at the start of the study. Ask if there is a family history of breast cancer: 3396of the 19,541women in the low-fat group and 4929of the 29,294women in the control group said “Yes.” If the random assignment worked well, there should not be a significant difference in the proportions with a family history of breast cancer.

(a) How significant is the observed difference? Carry out an appropriate test to help answer this question.

(b) Describe a Type I and a Type II error in this setting. Which is more serious? Explain.

See all solutions

Recommended explanations on Math Textbooks

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