Thread: Random sample

A simple random sample of size 10 drawn from a normal distribution yielded a sample mean of 100 and a sample variance of 64.

i) Obtain a 99% confidence interval for the true mean of the population
ii) What would the interval be if the population variance were known to be
σ^2 = 81?
iii) If it is required to be 95% confident that the sample mean is to be correct to within 2 euro of the true mean ,what samle size is necessary? Use σ^2 = 81.

Originally Posted by matty888

A simple random sample of size 10 drawn from a normal distribution yielded a sample mean of 100 and a sample variance of 64.

i) Obtain a 99% confidence interval for the true mean of the population
ii) What would the interval be if the population variance were known to be
σ^2 = 81?
iii) If it is required to be 95% confident that the sample mean is to be correct to within 2 euro of the true mean ,what samle size is necessary? Use σ^2 = 81.

I'll assume that you're familiar with the notation I use.


i)

where t follows a t-distribution with n - 1 degrees of freedom and is the critical value of t. In your case n = 10 and

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ii)

where z follows a standard normal distribution and is the critical value of z. In your case n = 10 and

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iii) Solve for n, where