Statistics

CHAPTER 8—Confidence Intervals

8.1 There is an entire population of possible sample means. A confidence interval is constructed to be confident that the true value of μ is contained in that interval.

LO1

8.2 95% of the time the interval formed will contain the population mean.

LO1

8.3 When the population standard deviation is known and the population is normal or n 30 or bigger

LO1

8.4 It gets longer (wider).

LO1

8.5 It gets shorter (narrower).

LO1

8.6

a.

b.

c.

d.

e.

f.

LO1

8.7 a.

b. Yes, 95% interval is above 50.

c. No, 99% interval extends below 50.

d. Fairly confident, since the 95% CI is above 50 while the 99% CI contains 50.

LO1

8.8 a.

b. Yes, 95% interval is below 6.

c. No, 99% interval extends above 6.

d. Fairly confident since 95% CI is below 6 while 99% CI contains 6.

LO1

8.9 a.

b. Yes, 95% interval is above 42.

c. Yes, 99% interval is above 42.

d. Very confident based on the 99% confidence interval being above 42.

LO1

8.10 a.

b.

c. Yes, confidence interval in (b) is totally above the confidence interval in (a).

LO1

8.11 a.

b.

c. Mean audit delay for public owner controlled companies appears to be shorter, since there is only a small amount of overlap of the intervals.

LO1

8.12 a.

b.

c. Mean number of dealers visited by late replacement buyers appears to be higher.

LO1

8.13 a. Decreases

b. Decreases

LO2

8.14 When is unknown, and the population you are sampling from is normal or approximately normal.

LO3

8.15 For 11 dfs

For 6 dfs

LO2

8.16 a.

b.

c.

d.

e.

f.

LO3

8.17 a.

b. Can be 95% confident the claim is true. Cannot be 99% confident the claim is true.

LO3

8.18 95% confidence interval:

No, lower end of confidence interval below 1 year. Sample size too small.

LO3

8.19 a.

b. Yes, 95% interval is below 8.

LO3...