Question 1

What sample size is needed to obtain a 95 percent confidence interval for the proportion of fat in meat that is within 3 percent of the true value?

Accepted Answer

n =≅ 1068

Question 2

You want to estimate the proportion of customers who are satisfied with their experiences at a local supermarket at α = .10 and within .025 of the true value. It has been estimated that p =.85. How large of a sample is needed?

Accepted Answer

n =≅ 553

Question 3

Find a 98 percent confidence interval for p when  = .25 and n = 400.

Accepted Answer

.25 ± 2.326→ .20 to .30

Question 4

What sample size is needed to estimate with 95 percent confidence the mean intake of daily calcium within 20 units of the true mean if the intake is normally distributed with a variance of 1900 units?

Accepted Answer

n == 19

Question 5

A cable TV company wants to estimate the percentage of cable boxes in use during an evening hour. An approximation is 20 percent. They want the estimate to be at the 90 percent confidence level and within 2 percent of the actual proportion. What sample size is needed?

Accepted Answer

n =≅ 1083

Question 6

The 95 percent confidence interval for the average weight of a product is from 72.23 lb to 77.77 lb. Is μ = 77 a possible population mean using that 95 percent confidence interval?

Accepted Answer

Yes, we can conclude that μ = 77, because it is in the interval.

Question 7

In a study of 265 engineering students, the average score on the final exam in the statistics course was 63.8 and s = 3.08. What is a 95 percent confidence for μ?

Accepted Answer

63.8 ± 1.96= 63.43 to 64.17

Question 8

The weight of a product is measured in pounds. A sample of 50 units is taken from a recent production. The sample yielded = 75 lb, and we know that σ² = 100 lb. Calculate a 99 percent confidence interval for μ.

Accepted Answer

75 ± 2.575⇒ 71.36 to 78.64

Question 9

The customer service manager for the XYZ Fastener Manufacturing Company examined 60 invoices and found 9 that contained errors. Find a 98 percent confidence interval for the proportion of invoices with errors.

Accepted Answer

== .15
.15 ± 2.326→ .043 to .257

Question 10

What sample size is needed to estimate the proportion of highway speeders within 5 percent using a 90 percent confidence level?

Accepted Answer

n =≅ 271

Question 11

In a randomly selected group of 650 automobile deaths, 180 were alcohol related. Construct a 95 percent confidence interval for the true proportion of all automobile accidents caused by alcohol.

Accepted Answer

== .2769
.2769 ± 1.96→ .243 to .311

Question 12

The weight of a product is measured in pounds. A sample of 50 units is taken from a recent production. The sample yielded = 75 lb, and we know that σ² = 100 lb. Calculate a 90 percent confidence interval for μ.

Accepted Answer

75 ± 1.645⇒ 72.67 to 77.33

Question 13

In a survey of 1,000 people, 420 are opposed to an income tax increase. Construct a 95 percent confidence interval for the proportion of people in the population opposed to this tax increase.

Accepted Answer

.42 ± 1.96→ .389 to .451

Question 14

The success rate of an experimental medical procedure is 37 per 120 cases in a sample. Find a 95 percent confidence interval for the actual success proportion of the procedure.

Accepted Answer

== .3083
.3083 ± 1.96→ .226 to .391

Question 15

What is a 95 percent confidence interval for μ when n = 10,  = 35.6, and s = 13.0? Assume population normality.

Accepted Answer

35.6 ± 2.262= 26.3 to 44.9

Question 16

What sample size is needed to obtain a 90 percent confidence interval for the mean protein content of meat if the estimate is to be within 2 pounds of the true mean value? Assume that the variance is 49 pounds.

Accepted Answer

n == 34

Question 17

The weight of a product is measured in pounds. A sample of 50 units is taken from a recent production. The sample yielded = 75 lb, and we know that σ² = 100 lb. Calculate a 95 percent confidence interval for μ.

Accepted Answer

75 ± 1.96⇒ 72.23 to 77.77

Question 18

We want to estimate with 99 percent confidence the percentage of automobile purchasers who are under 30 years of age. A margin of error of 5 percentage points is desired. What sample size is needed? In an earlier sample, we found a 99 percent confidence interval of purchasers under 30 years of age to be [.18, .27] (use this figure for the sample proportion).

Accepted Answer

n =≅ 463

Question 19

An insurance company estimates 45 percent of its claims have errors. The insurance company wants to estimate with 99 percent confidence the proportion of claims with errors. What sample size is needed if they wish to be within 5 percent of the actual?

Accepted Answer

n =≅ 657

Question 20

Given the following test scores, find a 95 percent confidence interval for the population mean: 148, 154, 158, 160, 161, 162, 166, 170, 182, 195, 236. Assume population normality.

Accepted Answer

172 ± 2.228(24.952/) = [155.24, 188.76]

Quiz 9: Confidence Intervals