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In: Statistics and Probability

In order to meet specifications, widgets must have a given time coefficient of at least 18....

In order to meet specifications, widgets must have a given time coefficient of at least 18. A sample of 100 widgets is drawn from the day’s production and tested and 21 of them had time coefficients less than 18.

a. Find a 98% confidence interval for the proportion of widgets manufactured that day which fail to meet specifications.

b. Repeat question a., but for 95% confidence interval.

c. For each of these two levels of confidence, find the sample size needed so that the corresponding confidence intervals specify the proportion to within ± 0.03.

d. If a 97% confidence interval is computed each day for 160 days, what is the probability that 154 of the computed confidence intervals cover the true proportion?

e. If a 97% confidence interval is computed each day for n days, to find the probability that at least 150 of the computed confidence intervals cover the true proportion, for what n > 150, can we safely utilize the normal approximation to the binomial? Justify your answer.

f. If a 97% confidence interval is computed each day for 500 days, what is the probability that at least 490 of the computed confidence intervals cover the true proportion?

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orchestra answered 2 years ago
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