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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.
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.