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# Hello, can someone help me solve these Statistics questions, please?

Hello, can someone help me solve these Statistics questions, please? If you can, please give me the detailed explanations with formulas because I am newbie and not good at Stat. Thank you so much!

**Question 1 **

Given a sample size of 16 from a normal distribution with a known variance of 25, yielded a sample mean equal to 14.5.

(i) Within what interval can we be 90% confident that μ lies?

(ii) Within what interval can we be 95% confident that μ lies?

(iii) From parts (i) and (ii), which interval is longer? Why?

**Question 2 **

A random sample of n = 25 work pieces had a mean diameter of 2mm. Based on the sample, s = 0.5. Set up a 95% confidence interval for the diameter.

**Question 3 **

A study conducted in a University showed that 41% of a sample of 1,110 people were likely to vote for Sarah if she stood against John in an election.

(i) Construct a 90% confidence interval for Sarah's chances in the election.

(ii) Construct a 95% confidence interval for Sarah's chances in the election.