A paper manufacturer has a production process that operates continuously throughout an entire production shift. The paper is expected to have a mean length of 8 inches, and the standard deviation of the length is 0.04 inch. At periodic intervals, a sample is selected to determine whether the mean paper length is still equal to 8 inches or whether something has gone wrong in the production process to change the length of the paper produced. A random sample of 100 sheets is selected, and the mean paper length is 7.938 inches. A 93% confidence interval estimate for the population mean paper length is 7.987682 mu 8.00832. Is it true that you do not know for sure whether the population mean is between 7.38768 and 8.00832 inches? Explain. Choose the correct answer below. It is false because the sample mean falls outside the interval. It is false because the sample mean falls within the interval. It is true because the population mean will be in the interval only 33% of the time. It is true because the population mean will be in the interval only 1% of the time. Why is it not possible to have 103% confidence? Explain. Choose the correct answer below. A 100% oonfiden.ee interval is not possible only if the entire population is sampled. 100% oonfiden.ee interval is not possible only if an absurdly wide interval of estimates is provided. 100% confidence interval is not possible unless either the entire population is sampled or an absurdly wide interval of estimates is provided. None of the above A market researcher selects a simple random sample of n= 100 users of a social media website from a population of over 100 million registered users. After analyzing the sample, she states that she has 35% confidence that the mean time spent on the site per day is between 15 and 57 minutes. Explain the meaning of this statement. Choose the correct answer below. There is a 35% chance that a randomly selected registered user spends between 15 and 57 minutes on the site per day. Of the over 103 million registered users, 95% of them spend between 15 and 57 minutes on the site per day. One is 35% confident that the true mean time all registered users spend on the site per day is between 15 and 57 minutes. During any given day there is a 95% chance that the mean time all registered users spent on the site was between 15 and 57 minutes.
1.
OPTION C: It is true as the population mean will be in the interval only 99% of the time.
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2.
OPTION C: A 100% confidence interval is not possible unless the entire population is samples or an absurdly wide intrval of estimates is provided.
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3.
OPTION C: One is 95% confident that the true mean time of all registered users spend on the site per day is between 15 and 57 minutes.
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4.
Note that
Lower Bound = X - z(alpha/2) * s / sqrt(n)
Upper Bound = X + z(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.005
X = sample mean = 122
z(alpha/2) = critical z for the confidence interval = 2.575829304
s = sample standard deviation = 24
n = sample size = 31
Thus,
Lower bound = 110.8968176
Upper bound = 133.1031824
Thus, the confidence interval is
( 110.8968176 , 133.1031824 ) [ANSWER]
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