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Chapter 12: Q. AP4.16 (page 829)

Two six-sided dice are rolled and the sum of the faces showing is recorded after each roll. Let X=the number of rolls required to obtain a sum greater than 7. If 100trials are conducted, which of the following is most likely to be the result of the simulation?

a.

b.

c.

d.

e.

Short Answer

Expert verified

The correct answer is option (a).

Step by step solution

01

Given information

X=the number of rolls required to obtain a sum greater than 7.

100 trials are conducted

02

Explanation

Two six-sided dice are tossed, with the sum of the faces shown being recorded after each roll.

Then, any choice other than (a) is invalid, because a sum higher than 7cannot be rolled with 0rolls.

Because the probability of getting a total larger than7 is extremely high, and not doing so on the first try gets increasingly implausible, the majority of trials only require one roll. As a result, option (a) is the proper choice.

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Most popular questions from this chapter

After a name-brand drug has been sold for several years, the Food and Drug Administration (FDA) will allow other companies to produce a generic equivalent. The FDA will permit the generic drug to be sold as long as there isn't convincing evidence that it is less effective than the name-brand drug. For a proposed generic drug intended to lower blood pressure, the following hypotheses will be us

where

渭G=true mean reduction in blood pressureusing the generic drug 渭G=true mean reduction in blood pressureusing the name@brand drug

渭G=true mean reduction in blood pressure

using the generic drug

渭G=true mean reduction in blood pressure

using the name@brand drug

In the context of this situation, which of the following describes a Type I error?

a. The FDA finds convincing evidence that the generic drug is less effective, when in reality it is less effective.

b. The FDA finds convincing evidence that the generic drug is less effective, when in reality it is equally effective.

c. The FDA finds convincing evidence that the generic drug is equally effective, when in reality it is less effective.

d. The FDA fails to find convincing evidence that the generic drug is less effective, when in reality it is less effective.

e. The FDA fails to find convincing evidence that the generic drug is less effective, when in reality it is equally effective.

Prey attracts predators Here is one way in which nature regulates the size of animal populations: high population density attracts predators, which remove a higher proportion of the population than when the density of the prey is low. One study looked at kelp perch and their common predator, the kelp bass. On each of four occasions, the researcher set up four large circular pens on sandy ocean bottoms off the coast of southern California. He randomly assigned young perch to 1of 4pens so that one pen had 10perch, one pen had 20perch, one pen had 40perch, and the final pen had 60perch. Then he dropped the nets protecting the pens, allowing bass to swarm in, and counted the number of perch killed after two hours. A regression analysis was performed on the16 data points using x=number of perch in pen and y=proportion of perch killed. Here is a residual plot and a histogram of the residuals. Check whether the conditions for performing inference about the regression model are met.


Here is computer output from the least-squares regression analysis of the perch data.

a. Find the critical value for a 90%confidence interval for the slope of the true regression line. Then calculate the confidence interval.

b. Interpret the interval from part (a).

c. Explain the meaning of 鈥�90% confident鈥� in this context.

T12.11 Growth hormones are often used to increase the weight gain of chickens. In an experiment using 15 chickens, 3 chickens were randomly assigned to each of 5 different doses of growth hormone (0, 0.2, 0.4, 0.8, and 1.0 milligrams). The subsequent weight gain (in ounces) was recorded for each chicken. A researcher plots the data and finds that a linear relationship appears to hold. Here is computer output from a least-squares
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a. Interpret each of the following in context:
i. The slope
ii. The y intercept
iii. The standard deviation of the residuals
iv. The standard error of the slope
b. Do the data provide convincing evidence of a linear relationship between dose and weight gain? Carry out a significance test at the 伪=0.05 level.
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Exercises T12.4鈥揟12.8 refer to the following setting. An old saying in golf is 鈥淵ou drive for show and you putt for dough.鈥� The point is that good putting is more important than long driving for shooting low scores and hence winning money. To see if this is the case, data from a random sample of 69 of the nearly 1000 players on the PGA Tour鈥檚 world money list are examined. The average number of putts per hole (fewer is better) and the player鈥檚 total winnings for the previous season are recorded and a least-squares regression line was fitted to the data. Assume the conditions for
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T12.6 The P -value for the test in Exercise T12.5 is 0.0087. Which of the following is a correct interpretation of this result?
a. The probability there is no linear relationship between average number of putts per hole and total winnings for these 69 players is 0.0087.
b. The probability there is no linear relationship between average number of putts per hole and total winnings for all players on the PGA Tour鈥檚 world money list is 0.0087.
c. If there is no linear relationship between average number of putts per hole and total winnings for the players in the sample, the probability of getting a random sample of 69 players that yields a least-squares regression line with a slope of 鈭�4,139,198 or less is 0.0087.
d. If there is no linear relationship between average number of putts per hole and total winnings for the players on the PGA Tour鈥檚 world money list, the probability of getting a random sample of 69 players that yields a least-squares regression line with a slope of 鈭�4,139,198 or less is 0.0087.
e. The probability of making a Type I error is 0.0087.

Prey attracts predators Here is one way in which nature regulates the size of animal populations: high population density attracts predators, which remove a higher proportion of the population than when the density of the prey is low. One study looked at kelp perch and their common predator, the kelp bass. On each of four occasions, the researcher set up four large circular pens on sandy ocean bottoms off the coast of southern California. He randomly assigned young perch to 1of 4pens so that one pen had 10perch, one pen had 20perch, one pen had 40perch, and the final pen had 60perch. Then he dropped the nets protecting the pens, allowing bass to swarm in, and counted the number of perch killed after two hours. A regression analysis was performed on the 16data points using x=number of perch in pen and y=proportion of perch killed. Here is a residual plot and a histogram of the residuals. Check whether the conditions for performing inference about the regression model are met.

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