Question 1

A survey of 100 fatal accidents showed that in 44 cases the driver at fault was inadequately insured. What is the point estimate for $$p$$, the population proportion of accidents where the driver at fault was inadequately insured?

Accepted Answer

$$0.44$$

Question 2

What is the critical value $$z_{\alpha/2}$$ for a 92% confidence level?

Accepted Answer

$$z_{\alpha/2} = 1.75$$

Question 3

A sample of 5700 people contains 20% successes. What is the margin of error $$E$$ for a 95% confidence interval for the population proportion? (Round to four decimal places.)

Accepted Answer

$$0.0104$$

Question 4

When 410 junior college students were surveyed, 185 said they have a passport. Construct a 95% confidence interval for the proportion of junior college students that have a passport. Which of the following is the correct interval (rounded to the nearest thousandth)?

Accepted Answer

$$0.398 \u003c p \u003c 0.502$$

Question 5

A researcher wants to estimate the proportion of adults in the U.S. with sleep deprivation. What is the minimum sample size needed to be 98% confident that the sample proportion will not differ from the true proportion by more than 5%?

Accepted Answer

$$n = 542$$

Question 6

Express the confidence interval $$0.148 \u003c p \u003c 0.652 in $$the form $$\hat{p} \pm E.$$

Accepted Answer

$$0.252 \pm 0.4$$

Question 7

Express the confidence interval $$0.469 \pm 0.077 in $$the form $$\hat{p} - E \u003c p \u003c \hat{p} + E.$$

Accepted Answer

$$0.392 \u003c p \u003c 0.469$$

Question 8

What is the minimum sample size required to estimate a population proportion with a margin of error $$E = 0.008$$, 99% confidence, and no prior estimate for $$p$$?

Accepted Answer

$$25,894$$

Question 9

A prior study estimates $$p = 0.52. $$What is the minimum sample size required to estimate the population proportion with a margin of error $$E = 0.02$$ and 95% confidence?

Accepted Answer

$$4,994$$

Question 10

How many women must be randomly selected to estimate the mean weight of women in one age group, with 90% confidence that the sample mean is within 2.7 lb of the population mean, given that the population standard deviation is 22 lb?

Accepted Answer

$$256$$

Question 11

A random sample of 104 test scores has a mean of $$95.3$$ and a standard deviation of $$6.5. $$What is the 99% confidence interval for the population mean $$\mu$$? (Round to one decimal place.)

Accepted Answer

$$93.0 \u003c \mu \u003c 97.6$$

Question 12

A random sample of 187 full-grown lobsters had a mean weight of 19 ounces. Assume the population standard deviation is 3.3 ounces. Construct a 98% confidence interval for the population mean $$\mu.$$

Accepted Answer

$$18.6 \u003c \mu \u003c 19.4$$

Question 13

A sample of $$n = 12$$ has a mean $$\bar{x} = 23.6$$ and sample standard deviation $$s = 6.6. $$What is the 99% confidence interval for the population mean $$\mu$$? (Assume normality.)

Accepted Answer

$$17.8 \u003c \mu \u003c 29.4$$

Question 14

A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 185 mg with $$s = 17.6 mg. $$Construct a 95% confidence interval for the true mean cholesterol content of all such eggs.

Accepted Answer

$$173.2 \u003c \mu \u003c 196.8$$

Question 15

Suppose you want to estimate the proportion of defective items produced by a factory. If you want to be 95% confident that your estimate is within 3% of the true proportion and you have no prior estimate for $$p$$, what is the minimum sample size required?

Accepted Answer

$$n = 1067$$

Question 16

A hospital administrator wants to estimate the average length of stay for patients. If the standard deviation is known to be 4 days, how large a sample is needed to be 99% confident that the sample mean is within 1 day of the population mean?

Accepted Answer

$$n = 107$$

Question 17

A company wants to estimate the mean time (in minutes) it takes to assemble a product. A sample of 36 workers has a mean of 42 minutes and a standard deviation of 6 minutes. What is the 95% confidence interval for the mean assembly time?

Accepted Answer

$$40.0 \u003c \mu \u003c 44.0$$

Question 18

A medical researcher wants to estimate the proportion of patients who respond positively to a new drug. If a previous study found $$p = 0.3$$, what sample size is needed to estimate the proportion within 4% with 95% confidence?

Accepted Answer

$$n = 504$$

Question 19

A pollster wants to estimate the proportion of voters who support a new policy. If the pollster wants to be 90% confident and the margin of error is 2%, with no prior estimate for $$p$$, what is the minimum sample size required?

Accepted Answer

$$n = 1691$$

Guided Practice: Confidence Intervals, Proportions, and Sample Size in Statistics

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