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# Confidence Interval, Sample Size & Margin of Error

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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 &#61555; = \$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, &#61549; 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 &#61555; 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 &#61549; 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.

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