# Chapter 7: Point Estimation and Sampling Distributions

1. Draw a random sample of *n* = 9 from the tv_hours data set (located on the companion website). Apply function data[sample(nrow(data),n ),]. Assign the values to the object named E7_1.

2. Draw a second random sample of *n* = 9. Use data[sample(nrow(data),n),]. Assign the values to the object named E7_2.

4. Referring to E7_1, E7_2, and the tv_hours data set, answer the following questions.

5. During the 2012 U.S. Presidential Election, 1,500 voters were interviewed upon exiting from a Manhattan polling station where they had just cast their votes. (The data set is named exit and is available on the companion website.) The data are recorded as a 1 for a Barack Obama vote and a 0 for a Mitt Romney vote. Draw a random sample of *n* = 25. Apply function data[sample(nrow(data),n),]; assign the values to the object named E7_3.

6. Draw a second random sample of *n* = 25 from exit and assign the values to the object named E7_4. (Remember: be sure to use the data[sample(nrow(data),n),] function.)

9. Suppose a random sample consists of the following 12 elements: 37, 14, 54, 91, 13, 88, 4, 16, 62, 18, 88, and 99. Copy and paste these values into the R Console and store them in an object named E7_5. Once this has been done, add the variable name values and create a data frame named E7_6. Answer the following questions using E7_6. (This exercise is intended to provide a bit of review of material covered earlier.)

10. When an Iberian tourism authority wanted to know from where travelers on one of their superhighways were coming, they monitored the bridge traffic connecting Castro Marim, Portugal with Ayamonte, Spain (crossing the River Guadiana). They found that for a random sample of 1,062 vehicles, 377 had Portuguese license plates while 418 had Spanish plates. The remaining 267 vehicles had plates from a country other than Spain or Portugal.

11. A random sample of size *n* = 36 is drawn from a population with a mean of *µ* = –17 and a standard deviation of *σ* = 6.

12. Suppose the mean level of debt carried by students graduating from U.S. universi- ties has now reached $27*, *000. Use this value as the population mean *µ *and assume that the population standard deviation is *σ *= $4*, *500. If a random sample of size *n *= 121 is selected, answer the following questions.

13. The provost at a large private university in the U.S. wishes to estimate the mean age for its 3,700 faculty members, and decides to draw a random sample of size *n* = 37 to derive the sample mean x̄.

14. A study reports that teenagers spend an average of 31 hours a week online and tex- ting. Assume that this is the population mean *µ*. Assume also that the population standard deviation is *σ *= 7 hours.

16. Suppose that in a study of faculty salaries at US-based graduate schools of management, the standard error of the mean is *σ*_{x̄} = $75 but the population standard deviation is *σ *= $4875.

18. Suppose a random sample of size *n *= 200 is drawn from a population with population proportion *p *= 0*.*55.

19. A random sample of size *n* = 100 is selected from a population with *p* = 0.60.

20. A population proportion is *p* = 0.50. Please provide the standard error of the proportion for the following sample sizes.

22. Assuming that the population proportion is *p* = 0.50, find *p*(0.49 ≤ ≤ 0.51) for each of the sample sizes below.

23. The percentage of people who are lefthanded is not known with certainty but it is thought to be about 12%. Assume the population proportion of lefthanded people is *p* = 0.12.