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Chapter 10: Q.3 (page 621)

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鈥檚 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鈥檚 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.

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Most popular questions from this chapter

One major reason that the two-sample t procedures are widely used is that they are quite robust. This means that

(a) t procedures do not require that we know the standard deviations of the populations.

(b) t procedures work even when the Random, Normal, and Independent conditions are violated.

(c) t procedures compare population means, a comparison that answers many practical questions.

(d) confidence levels and P-values from the t procedures are quite accurate even if the population distribution is not exactly Normal.

(e) confidence levels and P-values from the t procedures are quite accurate even if outliers and strong skewness are present

41. Literacy rates Do males have higher average literacy rates than females in Islamic countries? The table below shows the percent of men and women at least 15years old who were literate in 2008in the major Islamic nations. (We omitted countries with populations of less than3million.) Data for a few nations, such as Afghanistan and Iraq, were not available.

A driving school wants to find out which of its two instructors is more effective at preparing students to pass the state鈥檚 driver鈥檚 license exam. An incoming class of 100students is randomly assigned to two groups, each of size 50. One group is taught by Instructor A; the other is taught by Instructor B. At the end of the course, 30of Instructor A鈥檚 students and 22of Instructor B鈥檚 students pass the state exam. Do these results give convincing evidence that Instructor A is more effective?

Min Jae carried out the significance test shown below to answer this question. Unfortunately, he 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=0

Ha:p1-p2>0

where p1=the proportion of Instructor A's students that passed the state exam and p2=the proportion of Instructor B's students that passed the state exam. Since no significance level was stated, I'll use 蟽=0.05

Plan: If conditions are met, I鈥檒l do a two-sample ztest for comparing two proportions.

Random The data came from two random samples of 50students.

- Normal The counts of successes and failures in the two groups -30,20,22, and 28-are all at least 10.

- Independent There are at least 1000 students who take this driving school's class.

Do: From the data, p^1=2050=0.40and p^2=3050=0.60. So the pooled proportion of successes is

p^C=22+3050+50=0.52

- Test statistic

localid="1650450621864" z=(0.40-0.60)-00.52(0.48)100+0.52(0.48)100=-2.83

- p-value From Table A, localid="1650450641188" P(z鈮�-2.83)=1-0.0023=0.9977.

Conclude: The p-value, 0.9977, is greater than 伪=0.05, so we fail to reject the null hypothesis. There is no convincing evidence that Instructor A's pass rate is higher than Instructor B's.

T10.11. Researchers wondered whether maintaining a patient's body temperature close to normal by heating the patient during surgery would affect wound infection rates. Patients were assigned at random to two groups: the normothermic group (patients' core temperatures were maintained at near normal, 36.5掳C, with heating blankets) and the hypothermic group (patients" core temperatures were allowed to decrease to about34.5掳C). If keeping patients warm during surgery alters the chance of infection, patients in the two groups should have hospital stays of very different lengths. Here are summary statistics on hospital stay (in number of days) for the two groups:

Groupnx炉sxNormothemic10412.14.4Hypothermic9614.76.5

(a) Construct and interpret a 95%confidence interval for the difference in the true mean length of hospital stay for normothermic and hypothermic patients.

(b) Does your interval in part (a) suggest that keeping patients warm during surgery affects the average length of patients' hospital staves? Justify your answer.

A sample survey interviews SRSs of 500female college students and 550male college students. Each student is asked whether he or she worked for pay last summer. In all, 410 of the women and 484 of the men say 鈥淵es.鈥� The pooled sample proportion who worked last summer is about

(a) p铃�C=1.70

(b)p^C=0.89

(c) p^C=0.88

(d) p^C=0.85

(e) p^C=0.82
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