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99% confidence interval for the mean total fat

The data shown below represents the total fat, in grams per serving, for a sample of 20 chicken sandwiches from fast-food chains. Complete parts (a) through (d).

5 4 6 6 19 17 24 27 20 33
18 28 25 17 29 27 35 26 38 63

a. Construct a 99% confidence interval for the population mean total fat, in grams per serving.

b. Interpret the interval constructed in (a). Choose the correct answer below:
A. With 99% confidence, the mean amount of fat in the sample of chicken sandwiches is somewhere in the interval.
B. With 99% confidence, the mean amount of fat in the sample of chicken sandwiches is the population mean.
C. With 99% confidence, the mean amount of fat in the population of chicken sandwiches is somewhere in the interval.
D. With 99% confidence, the mean amount of fat in the population of chicken sandwiches is the sample mean.

c. What assumption must you make about the population distribution in order to construct the confidence interval estimate in (a)?
A. The population standard deviation is known.
B. The population distribution is uniformly distributed.
C. The population distribution needs to be normally distributed.
D. No assumptions are required.

d. Do you think that the assumption needed in order to construct the confidence interval estimate in (a) is valid? Explain.
A. No, because the distribution is not normally distributed.
B. Yes, because the distribution is normally distributed.
C. No, because the population standard deviation is not known.
D. Yes, because the population standard deviation is known.
E. Yes, because the distribution is uniformly distributed.
F. No, because the distribution is not uniformly distributed.
G. Yes, because no assumptions are required.

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Step-by-step calculation of 99% confidence interval for the mean total fat. Answers to the other questions are included.

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