Suppose a random sample of 10 fish are selected from a lake and their sample mean weight is 3.5 kg. Suppose the distribution of the weights of fish in the lake is normal and the population standard deviation is known to be 1 kg. (i). Construct a 95% confidence interval for the mean weight of all fish in the lake. Show your work. (ii). Write a two-sentence conclusion for the results of the confidence interval calculations. (iii). How large the sample size should be if we want the margin of error of a 95% confidence interval to be no more than 0.1? Show your work.

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Suppose a random sample of 10 fish are selected from a lake and
their sample mean weight is 3.5 kg. Suppose the distribution of the
weights of fish in the lake is normal and the population standard
deviation is known to be 1 kg.
(i). Construct a 95% confidence interval for the mean weight of all
fish in the lake. Show your work.
(ii). Write a two-sentence conclusion for the results of the confidence
interval calculations.
(iii). How large the sample size should be if we want the margin of
error of a 95% confidence interval to be no more than 0.1? Show
your work.
Transcribed Image Text:Suppose a random sample of 10 fish are selected from a lake and their sample mean weight is 3.5 kg. Suppose the distribution of the weights of fish in the lake is normal and the population standard deviation is known to be 1 kg. (i). Construct a 95% confidence interval for the mean weight of all fish in the lake. Show your work. (ii). Write a two-sentence conclusion for the results of the confidence interval calculations. (iii). How large the sample size should be if we want the margin of error of a 95% confidence interval to be no more than 0.1? Show your work.
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