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Chapter 5: Q63SE (page 323)

Improving SAT scores. Refer to the Chance(Winter2001) examination of Scholastic Assessment Test (SAT)scores of students who pay a private tutor to help them improve their results, Exercise 2.88 (p. 113). On the SAT鈥擬athematics test, these students had a mean score change of +19 points, with a standard deviation of 65 points. In a random sample of 100 students who pay a private tutor to help them improve their results, what is the likelihood that the sample mean score change is less than 10 points?

Short Answer

Expert verified

The likelihood that the sample means score change is less than 10 points is 0.0838.

Step by step solution

01

Given information

Referring to exercise 2.88 (p.113), there is a study about 100 students who pay a private tutor to help them improve their results. The students had a mean score of 19 and a standard deviation of 65 points.

02

Determine the likelihood

Let鈥檚 consider the sample mean of 渭x炉=19.

And the sample standard deviation of

蟽x炉=蟽n=65100=6.5

So, the likelihood that the sample mean score change is less than 10 points is,

PrX炉<10=PrX炉-渭x炉蟽x炉<10-196.5=Prz<-1.38=0.0838

Therefore, the likelihood is 0.0838.

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Most popular questions from this chapter

Switching banks after a merger. Banks that merge with others to form 鈥渕ega-banks鈥� sometimes leave customers dissatisfied with the impersonal service. A poll by the Gallup Organization found 20% of retail customers switched banks after their banks merged with another. One year after the acquisition of First Fidelity by First Union, a random sample of 250 retail customers who had banked with First Fidelity were questioned. Letp^ be the proportion of those customers who switched their business from First Union to a different bank.

  1. Find the mean and the standard deviation of role="math" localid="1658320788143" p^.
  2. Calculate the interval Ep^卤2蟽p^.
  3. If samples of size 250 were drawn repeatedly a large number of times and determined for each sample, what proportion of the values would fall within the interval you calculated in part c?

Consider the population described by the probability distribution shown below.

The random variable x is observed twice. If these observations are independent, verify that the different samples of size 2 and their probabilities are as shown below.

a. Find the sampling distribution of the sample meanx.

b. Construct a probability histogram for the sampling distribution ofx.

c. What is the probability thatxis 4.5 or larger?

d. Would you expect to observe a value ofxequal to 4.5 or larger? Explain.

Question:Stock market participation and IQ. Refer to The Journal of Finance (December 2011) study of whether the decision to invest in the stock market is dependent on IQ, Exercise 3.46 (p. 182). The researchers found that the probability of a Finnish citizen investing in the stock market differed depending on IQ score. For those with a high IQ score, the probability is .44; for those with an average IQ score, the probability is .26; and for those with a low IQ score, the probability is .14.

a. In a random sample of 500 Finnish citizens with high IQ scores, what is the probability that more than 150 invested in the stock market?

b. In a random sample of 500 Finnish citizens with average IQ scores, what is the probability that more than 150 invest in the stock market?

c. In a random sample of 500 Finnish citizens with low IQ scores, what is the probability that more than 150 invest in the stock market?

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.

Do social robots walk or roll? Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study of the trend in the design of social robots, Exercise 2.5 (p. 72). The researchers obtained a random sample of 106 social robots through a Web search and determined the number that was designed with legs but no wheels. Let p^represent the sample proportion of social robots designed with legs but no wheels. Assume that in the population of all social robots, 40% are designed with legs but no wheels.

a. Give the mean and standard deviation of the sampling distribution of p^.

b. Describe the shape of the sampling distribution of p^.

c. Find P(p^>.59).

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