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Chapter 5: Q30E (page 315)

Video game players and divided attention tasks. Human Factors (May 2014) published the results of a study designed to determine whether video game players are better than non鈥搗ideo game players at crossing the street when presented with distractions. Participants (college students) entered a street-crossing simulator. The simulator was designed to have cars traveling at various high rates of speed in both directions. During the crossing, the students also performed a memory task as a distraction. The researchers found that students who are video game players took an average of 5.1 seconds to cross the street, with a standard deviation of .8 second. Assume that the time, x, to cross the street for the population of video game players has , Now consider a sample of 30 students and let x represent the sample mean time (in seconds) to cross the street in the simulator.

a. Find Px炉>5.5

b. The 30 students in the sample are all non鈥搗ideo game players. What inference can you make about and/or for the population of non鈥搗ideo game players? Explain.

Short Answer

Expert verified

a. Probability of x炉 greater than 5.5 is 0.0031.

b. The population mean 渭for the non-video game players is greater than 5.1 and the population standard deviation 蟽for the non-video game players is greater than 0.8.

Step by step solution

01

Given information

A sample of 30 students is selected with mean 5.1 and the standard deviation 0.8.

02

Calculating the probability

a.

Let X be the time to cross the street in the simulator.

From the given problem 渭=5.1,蟽=0.8 and sample size is n=30.

According to Central limit theorem, if the sample size is large, then the sampling distribution of the sample meanx炉 becomes approximately normal.

Then

Px炉>5.5=Px炉-渭蟽/n>5.5-5.10.8/30=PZ>0.40.1461=PZ>2.74

=1-PZ猢�2.74=1-0.5+P0<Z<2.74=1-0.5-0.4969=0.0031

Thus, Px炉>5.5=0.0031

03

Interpretation

b.

From part a., the probability that sample mean is greater than 5.5 is 0.0031. Moreover, the probability for the video game players is very low than the non-video game players. Thus, the population mean 渭for the non-video game players is greater than 5.1 and the population standard deviation蟽 for the non-video game players is greater than 0.8.

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Most popular questions from this chapter

Length of job tenure. Researchers at the Terry College ofBusiness at the University of Georgia sampled 344 business students and asked them this question: 鈥淥ver the course of your lifetime, what is the maximum number of years you expect to work for any one employer?鈥� The sample resulted in x= 19.1 years. Assume that the sample of students was randomly selected from the 6,000 undergraduate students atthe Terry College and that = 6 years.

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  3. If a sample of n = 2 measurements is randomly selected from the population, what is the probability that a specific sample will be selected.
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