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Chapter 12: Q. AP4.25 (page 831)

Suppose that the mean weight of a certain breed of pig is 280pounds with a standard deviation of 80pounds. The distribution of weight for these pigs tends to be somewhat skewed to the right. A random sample of 100pigs is taken. Which of the following statements about the sampling distribution of the sample mean weight xis true?

a. It will be Normally distributed with a mean of 280pounds and a standard deviation of 80pounds.

b. It will be Normally distributed with a mean of 280pounds and a standard deviation of 8pounds.

c. It will be approximately Normally distributed with a mean of 280pounds and a standard deviation of80pounds.

d. It will be approximately Normally distributed with a mean of 280pounds and a standard deviation of 8pounds.

e. There is not enough information to determine the mean and standard deviation of the sampling distribution.

Short Answer

Expert verified

The correct answer is option (d) It will be approximately Normally distributed with a mean of 280pounds and a standard deviation of 8pounds.

Step by step solution

01

Concept introduction

In quantitative tests, segmentation is the technique of selecting a predefined dataset from a huge population. Vary based on the type of assessment being undertaken, the measures taken to recruit from a general community may include simple chance picking or multi - stage sampling.

02

Explanation

Assume that the mean weight of a specific trait of pig is 280pounds, with a 80pound confidence interval. The weight distribution for these pigs is somewhat biased to the right.

As a result, the incidence will be essentially normal. We cannot assert that the probability is perfectly normal, but because n>30, we may say that it is normally distributed according to the central limit theorem. As a result,

σ=80100=8μ=280

Option (d) is correct

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Most popular questions from this chapter

Exercises T12.4–T12.8 refer to the following setting. An old saying in golf is “You drive for show and you putt for dough.” 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’s world money list are examined. The average number of putts per hole (fewer is better) and the player’s total winnings for the previous season are recorded and a least-squares regression line was fitted to the data. Assume the conditions for
inference about the slope are met. Here is computer output from the regression analysis:

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’s 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 −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’s world money list, the probability of getting a random sample of 69 players that yields a least-squares regression line with a slope of −4,139,198 or less is 0.0087.
e. The probability of making a Type I error is 0.0087.

Could mud wrestling be the cause of a rash contracted by University of Washington students? Two physicians at the university’s student health center wondered about this when one male and six female students complained of rashes after participating in a mud-wrestling event. Questionnaires were sent to a random sample of students who participated in the event. The results, by gender, are summarized in the following table.

Here is some computer output for the preceding table. The output includes the observed counts, the expected counts, and the chi-square statistic.

From the chi-square test performed in this study, we may conclude that

a. there is convincing evidence of an association between the gender of an individual participating in the event and the development of a rash.

b. mud wrestling causes a rash, especially for women.

c. there is absolutely no evidence of any relationship between the gender of an individual participating in the event and the subsequent development of a rash.

d. development of a rash is a real possibility if you participate in mud wrestling, especially if you do so regularly.

e. the gender of the individual participating in the event and the development of a rash are independent.

Women who are severely overweight suffer economic consequences, a study has shown. They have household incomes that are $6710less than other women, on average. The findings are from an eight-year observational study of 10,039randomly selected women who were 16-24years old when the research began. If the difference in average incomes is statistically significant, does this study give convincing evidence that being severely overweight causes a woman to have a lower income?

a. Yes; the study included both women who were severely overweight and women who were not.

b. Yes; the subjects in the study were selected at random.

c. Yes, because the difference in average incomes is larger than would be expected by chance alone.

d. No; the study showed that there is no connection between income and being severely overweight.

e. No; the study suggests an association between income and being severely overweight, but we can’t draw a cause-and-effect conclusion.

Which of the following is a categorical variable?

a. The weight of an automobile

b. The time required to complete the Olympic marathon

c. The fuel efficiency (in miles per gallon) of a hybrid car

d. The brand of shampoo purchased by shoppers in a grocery store

e. The closing price of a particular stock on the New York Stock Exchange

Beer and BAC How well does the number of beers a person drinks predict his or her blood alcohol content (BAC)? Sixteen volunteers aged 21or older with an initial BAC of 0took part in a study to find out. Each volunteer drank a randomly assigned number of cans of beer. Thirty minutes later, a police officer measured their BAC. A least-squares regression analysis was performed on the data using x=number of beers and y=BAC. 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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