Question

In: Statistics and Probability

I am stuck on the following review problem on confidence intervals. Could you please guide me...

I am stuck on the following review problem on confidence intervals. Could you please guide me on how to approach this type of problem?

A bakery does not keep track of the number of chocolate chips they put in their cookies. The number of chocolate chips is normally distributed with mean µ and variance σ2 = 25, where µ is unknown. A customer buys a dozen of these cookies, and obtains the simple random sample 31, 23, 42, 44, 28, 34, 19, 29, 30, 25, 28, 27

(a) Compute a 95% confidence interval for µ.

(b) Compute 90% and 99% confidence intervals for µ.

(c) Suppose the customer wants a 95% confidence interval that has a width of at most 2. How many cookies would he need to buy to achieve this?

Solutions

Expert Solution

Solution:

a) 95% CI for u is:

b) 90% and 99% CI for u are:

c) given, width=2 i.e. MOE= width/2= 2/2= 1

orchestra answered 2 years ago
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