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Chapter 6: Q.32 (page 357)

Chess and reading (4.3) If the study found a statistically significant improvement in reading scores, could you conclude that playing chess causes an increase in reading skills? Justify your answer

Short Answer

Expert verified

No. It cannot be concluded that playing chess is leading to an increase in reading skills.

Step by step solution

01

Given Information

It is given in the question that,

The graphs and numerical summaries below provide information on the subjects’ pretest scores, posttest scores, and the difference (post – pre) between these two scores.

02

Explanation

There are no specifics about the sample selection procedure provided here. As a result, it is impossible to say whether the chosen sample is random or not, and an overall picture of the population cannot be constructed without knowing the selection technique.

Furthermore, importance does not always imply causality.

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Most popular questions from this chapter

Blood types In the United States, 44%of adults have type O blood. Suppose we choose 7U.S. adults at random. Let X=the number who have type O blood. Use the binomial probability formula to find P(X=4). Interpret this result in context.

Exercises 47 and 48 refer to the following setting. Two independent random variables Xand Yhave the probability distributions, means, and standard deviations shown.

47. Sum Let the random variableT=X+Y.
(a) Find all possible values of T. Compute the probability that Ttakes each of these values. Summarize the probability distribution ofT in a table.
(b) Show that the mean of Tis equal toμX+μY.
(c) Confirm that the variance of T is equal to σX2+σY2. Show that σT≠σX+σY.

78. Rhubarb Refer to Exercise 76. Would you be surprised if 3 or more of the plants in the bundle die before producing any rhubarb? Calculate an appropriate probability to support your answer.

A deck of cards contains 52cards, of which 4are aces. You are offered the following wager: Draw one card at random from the deck. You win \(10if the card drawn is an ace. Otherwise, you lose \)1. If you make this wager very many times, what will be the mean amount you win?

(a) About −\(1, because you will lose most of the time.

(b) About \)9, because you win \(10but lose only \)1.

(c) About −\(0.15; that is, on average you lose about 15cents. (d) About \)0.77; that is, on average you win about 77cents.

(e) About $0, because the random draw gives you a fair bet.

Benford’s law and fraud A not-so-clever employee decided to fake his monthly expense report. He believed that the first digits of his expense amounts should be equally likely to be any of the numbers from 1to 9. In that case, the first digit Yof a randomly selected expense amount would have the probability distribution shown in the histogram.

(a). Explain why the mean of the random variable Y is located at the solid red line in the figure.

(b) The first digits of randomly selected expense amounts actually follow Benford’s law (Exercise 5). What’s the expected value of the first digit? Explain how this information could be used to detect a fake expense report.

(c) What’s P(Y>6)? According to Benford’s law, what proportion of first digits in the employee’s expense amounts should be greater than 6? How could this information be used to detect a fake expense report?
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