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2. A sample of 16 weeks’ worth of sales shows mean sales of 100 units. Assume...

2. A sample of 16 weeks’ worth of sales shows mean sales of 100 units. Assume the population standard deviation is 16 units. Construct a 95% confidence interval for the weekly number of units sold.

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We will use z distribution in this case because we know that when the population standard deviation known, we use z distribution.

So, the formula confidence interval is given as

CI = mu pm z*(sigma/sqrt{n})

where mu = mean = 100, sigma =16, n=16

sigma is standard deviation and n is sample size

z score for 95% confidence interval is 1.96 (using z distribution table)

setting the given values in the above formula

we get

C1 = 100土1.96 * (16/v/16) = 100士1.96 * (16/4) = 100 ± (1.96 * 4)

this gives us

CI = (100-7.84, 100+7.84) = (92.16,107.84)

So, the required 95% confidence interval is (92.16,107.84)

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