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# Confidence interval, true mean and sample size calculation

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8.46 A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were
3.087, 3.131, 3.241, 3.241, 3.270, 3.353, 3.400, 3.411, 3.437, 3.477
(a) Construct a 90 percent confidence interval for the true mean weight. (b) What sample size would be necessary to estimate the true weight with an error of ± 0.03 grams with 90 percent confidence? (c) Discuss the factors which might cause variation in the weight of Tootsie Rolls during manufacture

8.62 In 1992, the FAA conducted 86,991 pre-employment drug tests on job applicants who were to be engaged in safety and security-related jobs, and found that 1,143 were positive. (a) Construct a 95 percent confidence interval for the population proportion of positive drug tests. (b) Why is the normality assumption not a problem, despite the very small value of p?

https://brainmass.com/statistics/confidence-interval/confidence-interval-true-mean-and-sample-size-calculation-171876

#### Solution Summary

This solution has step-by-step method in excel sheet for constructing a confidence interval for different percentages and sample sizing for estimating true mean weight. It also discusses the factors that cause variations in a manufacturing process.

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## Confidence Interval & Sample Size for a Random Sample

1 (b). A survey of a random sample of 250 car commuters indicates that 80 would switch to commuting by public transport if they had to pay at least \$10 per week for parking at their work places.

(i) Using a 95% confidence level, calculate the confidence interval for the proportion of the commuters who might be expected to change to using public transport for the journey-to-work.

(ii) Comment on the relationship between sample size and margin of error.

(c) Suppose we want to estimate, with 95% confidence, the percentage of commuters who would change to using public transport for the journey-to-work with a margin of error of +-3%. How large a sample of people will need to be taken:

(i) A preliminary estimate suggests that the true percentage is about 32%.

(ii) No preliminary estimate is available.

see attached file.

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