We have the following six randomly drawn observations from an underlying normal distribution with unknown expectation &#

[answerhappygod]

We have the following six randomly drawn observations from an underlying normal distribution with unknown
expectation 𝜇 and unknown variance 𝜎2: 31,32,30,31,29,30.

a) Find a 95% confidence interval for 𝜇 based on the observations
Tip: Variance 𝜎2 is unknown and must be estimated. .

The data in problem a) are considered a pilot study to estimate the standard deviation of
the normal distribution. Now you are planning a major survey where the confidence interval is required
for 𝜇 shall be less than 𝐿 = 0.2.

b) How many observations do you need? Tip: now you can assume that the variance is known and that it is equal
the estimate from problem a).