Deck 8: Estimation

Question 1

A random sample of 360 medical doctors showed that 106 had a solo practice. As a news writer, how would you report the survey results regarding the percentage of medical doctors in solo practice? What is the margin of error based on a 95% confidence interval?

A)A recent study shows that about 71% of medical doctors have a solo practice with a margin of error of 2.4 percentage points.
B)A recent study shows that about 29% of medical doctors have a solo practice with a margin of error of 9.4 percentage points.
C)A recent study shows that about 71% of medical doctors have a solo practice with a margin of error of 9.4 percentage points.
D)A recent study shows that about 71% of medical doctors have a solo practice with a margin of error of 4.7 percentage points.
E)A recent study shows that about 29% of medical doctors have a solo practice with a margin of error of 4.7 percentage points.

Answer 1

A recent study shows that about 29% of medical doctors have a solo practice with a margin of error of 4.7 percentage points.

Question 2

In a random sample of 88 professional actors, it was found that 20 were extroverts. Let p represent the proportion of all actors who are extroverts. Find a point estimate for p.

A)68
B)0.227
C)20
D)0.114
E)0.773

Answer 2

0.227

Question 3

Suppose the method of tree ring dating gave the following dates A.D. for an archaeological excavation site. Find an 80% confidence interval for the mean of all tree ring dates from this archaeological site.
1273 $\quad$ 1231 $\quad$ 1173 $\quad$ 1228 $\quad$ 1191 $\quad$ 1206 $\quad$ 1194 $\quad$ 1227 $\quad$ 1261

A)1205.3 to 1234.9
B)1205.3 to 1235.8
C)1206.0 to 1235.8
D)1205.1 to 1235.8
E)1205.3 to 1235.6

Answer 3

1205.1 to 1235.8

Question 4

Suppose a certain species bird has an average weight of grams. Based on previous studies, we can assume that the weights of these birds have a normal distribution with grams. Find the sample size necessary for a 95% confidence level with a maximal error of estimate for the mean weights of the hummingbirds. $$\bar { x } = 3.60$$ $$\sigma = 0.36$$ $$E = 0.18$$

A)61
B)31
C)4
D)16
E)8

Question 5

In a random sample of 31 professional actors, it was found that 24 were extroverts. Find a 98% confidence interval for p.

A)0.589 to 0.959
B)0.647 to 1.485
C)0.647 to 0.902
D)0.589 to 1.485
E)0.063 to 0.959

Question 6

Suppose a certain species bird has an average weight of grams. Based on previous studies, we can assume that the weights of these birds have a normal distribution with grams. For a small group of 12 birds, find the margin of error for an 80% confidence interval for the average weights of these birds. $$\bar { x } = 3.45$$ $$\sigma = 0.34$$

A)0.22 grams
B)0.13 grams
C)0.02 grams
D)0.44 grams
E)0.06 grams

Question 7

A random sample of medical files is used to estimate the proportion p of all people who have blood type B. If you have no preliminary estimate for p, how many medical files should you include in a random sample in order to be 95% sure that the point estimate will be within a distance of 0.04 from p? $\hat { p }$

A)2401
B)25
C)13
D)1201
E)601

Question 8

Suppose forty communities have an average of reported cases of larceny per year. Assume that $\sigma$ is known to be 39.7 cases per year. Find an 85%, 90%, and 98% confidence interval for the population mean annual number of reported larceny cases in such communities. Compare the margins of error. As the confidence level increase, do the margins of error increase? $$\bar { x } = 134.7$$

A)The 85% confidence level has a margin of error of 57.2; the 90% confidence level has a margin of error of 65.3; and the 98% confidence level has a margin of error of 92.5. As the confidence level increases, the margins of error increase.
B)The 85% confidence level has a margin of error of 9.0; the 90% confidence level has a margin of error of 10.3; and the 98% confidence level has a margin of error of 14.6. As the confidence level increases, the margins of error increase.
C)The 85% confidence level has a margin of error of 1.4; the 90% confidence level has a margin of error of 1.6; and the 98% confidence level has a margin of error of 2.3. As the confidence level increases, the margins of error increase.
D)The 85% confidence level has a margin of error of 14.6; the 90% confidence level has a margin of error of 10.3; and the 98% confidence level has a margin of error of 9.0. As the confidence level increases, the margins of error decrease.
E)The 85% confidence level has a margin of error of 92.5; the 90% confidence level has a margin of error of 65.3; and the 98% confidence level has a margin of error of 57.2. As the confidence level increases, the margins of error decrease.

Question 9

Suppose twenty-seven communities have an average of reported cases of larceny per year. Assume that $\sigma$ is known to be 41.7 cases per year. Find an 80%, 90%, and 95% confidence interval for the population mean annual number of reported larceny cases in such communities. Compare the lengths of the confidence intervals. As the confidence levels increase, do the confidence intervals increase in length? $$\bar { x } = 133.5$$

A)The 80% confidence level has a confidence interval length of 6.1; the 90% confidence level has a confidence interval length of 5.1; and the 95% confidence level has a confidence interval length of 4.0. As the confidence level increases, the confidence interval length decreases.
B)The 80% confidence level has a confidence interval length of 106.8; the 90% confidence level has a confidence interval length of 137.2; and the 95% confidence level has a confidence interval length of 163.5. As the confidence level increases, the confidence interval length increases.
C)The 80% confidence level has a confidence interval length of 4.0; the 90% confidence level has a confidence interval length of 5.1; and the 95% confidence level has a confidence interval length of 6.1. As the confidence level increases, the confidence interval lengths increases.
D)The 80% confidence level has a confidence interval length of 163.5; the 90% confidence level has a confidence interval length of 137.2; and the 95% confidence level has a confidence interval length of 106.8. As the confidence level increases, the confidence interval lengths decreases.
E)The 80% confidence level has a confidence interval length of 20.5; the 90% confidence level has a confidence interval length of 26.4; and the 95% confidence level has a confidence interval length of 31.5. As the confidence level increases, the confidence interval lengths increases.