10-7. Exercises

1. BASIC

For the Basic and Application exercises in this section use the computations that were done for the exercises with the same number in previous sections.

Ex 1. For the sample data set of Exercise 1 of Section 10.2 "The Linear Correlation Coefficient"

1. Give a point estimate for the mean value of $y$ in the sub-population determined by the condition $x = 4$ .

2. Construct the 90% confidence interval for that mean value.

Ex 2. For the sample data set of Exercise 2 of Section 10.2 "The Linear Correlation Coefficient"

1. Give a point estimate for the mean value of $y$ in the sub-population determined by the condition $x = 4$ .

2. Construct the 90% confidence interval for that mean value.

Ex 3. For the sample data set of Exercise 3 of Section 10.2 "The Linear Correlation Coefficient"

1. Give a point estimate for the mean value of $y$ in the sub-population determined by the condition $x = 7$ .

2. Construct the 95% confidence interval for that mean value.

Ex 4. For the sample data set of Exercise 4 of Section 10.2 "The Linear Correlation Coefficient"

1. Give a point estimate for the mean value of $y$ in the sub-population determined by the condition $x = 2$ .

2. Construct the 80% confidence interval for that mean value.

Ex 5. For the sample data set of Exercise 5 of Section 10.2 "The Linear Correlation Coefficient"

1. Give a point estimate for the mean value of $y$ in the sub-population determined by the condition $x = 1$ .

2. Construct the 80% confidence interval for that mean value.

Ex 6. For the sample data set of Exercise 6 of Section 10.2 "The Linear Correlation Coefficient"

1. Give a point estimate for the mean value of $y$ in the sub-population determined by the condition $x = 5$ .

2. Construct the 95% confidence interval for that mean value.

Ex 7. For the sample data set of Exercise 7 of Section 10.2 "The Linear Correlation Coefficient"

1. Give a point estimate for the mean value of $y$ in the sub-population determined by the condition $x = 6$ .

2. Construct the 99% confidence interval for that mean value.

3. Is it valid to make the same estimates for $x = 12$ ? Explain.

Ex 8. For the sample data set of Exercise 8 of Section 10.2 "The Linear Correlation Coefficient"

1. Give a point estimate for the mean value of $y$ in the sub-population determined by the condition $x = 12$ .

2. Construct the 80% confidence interval for that mean value.

3. Is it valid to make the same estimates for $x = 0$ ? Explain.

Ex 9. For the sample data set of Exercise 9 of Section 10.2 "The Linear Correlation Coefficient"

1. Give a point estimate for the mean value of $y$ in the sub-population determined by the condition $x = 0$ .

2. Construct the 90% confidence interval for that mean value.

3. Is it valid to make the same estimates for $x=−1$ ? Explain.

Ex 10. For the sample data set of Exercise 9 of Section 10.2 "The Linear Correlation Coefficient"

1. Give a point estimate for the mean value of $y$ in the sub-population determined by the condition $x = 8$ .

2. Construct the 95% confidence interval for that mean value.

3. Is it valid to make the same estimates for $x = 0$ ? Explain.

2. APPLICATIONS

Ex 11. For the data in Exercise 11 of Section 10.2 "The Linear Correlation Coefficient"

1. Give a point estimate for the average number of words in the vocabulary of 18-month-old children.

2. Construct the 95% confidence interval for that mean value.

3. Is it valid to make the same estimates for two-year-olds? Explain.

Ex 12. For the data in Exercise 12 of Section 10.2 "The Linear Correlation Coefficient"

1. Give a point estimate for the average braking distance of automobiles that weigh 3,250 pounds.

2. Construct the 80% confidence interval for that mean value.

3. Is it valid to make the same estimates for 5,000-pound automobiles? Explain.

Ex 13. For the data in Exercise 13 of Section 10.2 "The Linear Correlation Coefficient"

1. Give a point estimate for the resting heart rate of a man who is 35 years old.

2. One of the men in the sample is 35 years old, but his resting heart rate is not what you computed in part (a). Explain why this is not a contradiction.

3. Construct the 90% confidence interval for the mean resting heart rate of all 35-year-old men.

Ex 14. For the data in Exercise 14 of Section 10.2 "The Linear Correlation Coefficient"

1. Give a point estimate for the wave height when the wind speed is 13 miles per hour.

2. One of the wind speeds in the sample is 13 miles per hour, but the height of waves that day is not what you computed in part (a). Explain why this is not a contradiction.

3. Construct the 90% confidence interval for the mean wave height on days when the wind speed is 13 miles per hour.

Ex 15. For the data in Exercise 15 of Section 10.2 "The Linear Correlation Coefficient"

1. The business owner intends to spend $2,500 on advertising next year. Give an estimate of next year’s revenue based on this fact.

2. Construct the 90% prediction interval for next year’s revenue, based on the intent to spend $2,500 on advertising.

Ex 16. For the data in Exercise 16 of Section 10.2 "The Linear Correlation Coefficient"

1. A two-year-old girl is 32.3 inches long. Predict her adult height.

2. Construct the 95% prediction interval for the girl’s adult height.

Ex 17. For the data in Exercise 17 of Section 10.2 "The Linear Correlation Coefficient"

1. Lodovico has a 78.6 average in his physics class just before the final. Give a point estimate of what his final exam grade will be.

2. Explain whether an interval estimate for this problem is a confidence interval or a prediction interval.

3. Based on your answer to (b), construct an interval estimate for Lodovico’s final exam grade at the 90% level of confidence.

Ex 18. For the data in Exercise 18 of Section 10.2 "The Linear Correlation Coefficient"

1. This year 86.2 million acres of corn were planted. Give a point estimate of the number of acres that will be harvested this year.

2. Explain whether an interval estimate for this problem is a confidence interval or a prediction interval.

3. Based on your answer to (b), construct an interval estimate for the number of acres that will be harvested this year, at the 99% level of confidence.

Ex 19. For the data in Exercise 19 of Section 10.2 "The Linear Correlation Coefficient"

1. Give a point estimate for the blood concentration of the active ingredient of this medication in a man who has consumed 1.5 ounces of the medication just recently.

2. Gratiano just consumed 1.5 ounces of this medication 30 minutes ago. Construct a 95% prediction interval for the concentration of the active ingredient in his blood right now.

Ex 20. For the data in Exercise 20 of Section 10.2 "The Linear Correlation Coefficient"

1. You measure the girth of a free-standing oak tree five feet off the ground and obtain the value 127 inches. How old do you estimate the tree to be?

2. Construct a 90% prediction interval for the age of this tree.

Ex 21. For the data in Exercise 21 of Section 10.2 "The Linear Correlation Coefficient"

1. A test cylinder of concrete three days old fails at 1,750 psi. Predict what the 28-day strength of the concrete will be.

2. Construct a 99% prediction interval for the 28-day strength of this concrete.

3. Based on your answer to (b), what would be the minimum 28-day strength you could expect this concrete to exhibit?

Ex 22. For the data in Exercise 22 of Section 10.2 "The Linear Correlation Coefficient"

1. Tomorrow’s average temperature is forecast to be 53 degrees. Estimate the energy demand tomorrow.

2. Construct a 99% prediction interval for the energy demand tomorrow.

3. Based on your answer to (b), what would be the minimum demand you could expect?

3. LARGE DATA SET EXERCISES

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Ex 23. Large Data Set 1 lists the SAT scores and GPAs of 1,000 students.

1. Give a point estimate of the mean GPA of all students who score 1350 on the SAT.

2. Construct a 90% confidence interval for the mean GPA of all students who score 1350 on the SAT.

Ex 24. Large Data Set 12 lists the golf scores on one round of golf for 75 golfers first using their own original clubs, then using clubs of a new, experimental design (after two months of familiarization with the new clubs).

1. Thurio averages 72 strokes per round with his own clubs. Give a point estimate for his score on one round if he switches to the new clubs.

2. Explain whether an interval estimate for this problem is a confidence interval or a prediction interval.

3. Based on your answer to (b), construct an interval estimate for Thurio’s score on one round if he switches to the new clubs, at 90% confidence.

Ex 25. Large Data Set 13 records the number of bidders and sales price of a particular type of antique grandfather clock at 60 auctions.

1. There are seven likely bidders at the Verona auction today. Give a point estimate for the price of such a clock at today’s auction.

2. Explain whether an interval estimate for this problem is a confidence interval or a prediction interval.

3. Based on your answer to (b), construct an interval estimate for the likely sale price of such a clock at today’s sale, at 95% confidence.