# Confidence Interval, Sample Size & Margin of Error

Section 6.1: Confidence Intervals for the Mean (Large Samples)

1. Find the critical value zc necessary to form a confidence interval at the given level of confidence. (References: definition for level of confidence page 311, end of section exercises 5 - 8 page 317)

a. 98%

b. 95%

2. In a random sample of 60 computers, the mean cost for repairs was $150. From past studies, it was found that the standard deviation was  = $36.

(References: example 5 page 315, end of section exercises 51 - 56 pages 319 - 320)

a. Find the margin of error E for a 90% confidence interval.

Round your answer to the nearest hundredths. . (References:

definition of margin of error on page 312 and example 2 on

page 312).

b. Construct a 90% confidence interval for the mean life,  of repair costs.

3. A nurse at a local hospital is interested in estimating the birth weight of infants. How large a sample must she select if she desires to be 98% confident that the true mean is within 3 ounces of the sample mean? The standard deviation  is known to be 6 ounces. (References: example 6 page 316, end of section exercises 58 - 62 pages 321 - 322)

Section 6.2: Confidence Intervals for the Mean (Small Samples)

4. A random sample of 16 fluorescent light bulbs has a mean life of 645 hours with a sample standard deviation of 31 hours. Assume the population has a normal distribution.(References: example 2 and 3 pages 327 - 328, end of section exercises 5 - 16 pages 330 - 331)

a. Find the margin of error for a 95% confidence interval. Round your answer to the nearest tenths.

b. Find a 95% confidence interval for the mean  for all fluorescent light bulbs.

Section 6.3: Confidence Intervals for Population Proportions

5. In a survey of 2480 golfers, 15% said they were left-handed. Construct to the 95% confidence interval for the population proportion p. (References: example 1 - 3 page 334 - 337, end of section exercises 13 - 20 page 339 - 340)

a. Find the margin of error E.

Round E to three decimal places

c. Construct a 95% confidence interval for the population proportion p of left-handed golfers.

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#### Solution Summary

The solution provides step by step method for the calculation of confidence interval, sample size and margin of error. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

Statistics 7 questions: Confidence interval, sample mean, deviation, margin of error

1. An election poll reported that a candidate had an approval rating of 45% with a margin of error E of 4%. Construct a confidence interval for the proportion of adults who approve of the candidate.

The confidence interval for the proportion of adults who approve of the candidate is ____

(Round to two decimal places as needed.)

2. You are given the sample mean and the sample standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Which interval is wider? If convenient, use technology to construct the confidence intervals.

A random sample of 48 eight-ounce servings of different juice drinks has a mean of 97.3 calories and a standard deviation of 47.6 calories.

The 90% confidence interval is _____. (Round to one decimal place as needed.)

The 95% confidence interval is _____. (Round to one decimal place as needed.)

Which interval is wider?

3. The state test scores for 12 randomly selected high school seniors are shown on the right.

1422 1224 989

696 729 839

725 749 540

627 1441 940

Assume the population is normally distributed.

(a) Find the sample mean.

x-bar = ______ (Round to one decimal place as needed.)

(b) Find the sample standard deviation.

s = ________ (Round to one decimal place as needed.)

(c) Construct a 99% confidence interval for the population mean µ.

A 99% confidence interval for the population mean is ______

(Round to one decimal place as needed.)

4. A researcher wishes to estimate, with 95% confidence, the proportion of adults who have high-speed Internet access. Her estimate must be accurate within 3% of the true proportion.

(a) Find the minimum sample size needed, using a prior study that found that 56% of the respondents said they have high-speed Internet access?

n = ____ (Round up to the nearest whole number as needed.)

(b) What is the minimum sample size needed assuming that no preliminary estimate is available?

n = ____ (Round up to the nearest whole number as needed.)

5. People were polled on how many books they read the previous year. How many subjects are needed to estimate the number of books read the previous year within one book with 90% confidence? Initial survey results indicate that σ = 18.6 books.

A 90% confidence level requires __________ subjects.

(Round up to the nearest whole number as needed.)

6. Use the confidence interval to find the estimated margin of error. Then find the sample mean.

A biologist reports a confidence interval of (1.9, 3.3) when estimating the mean height (in centimeters) of a sample of seedlings.

The estimated margin of error is _________.

The sample mean is _________.

See attached file.

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