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!
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?
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.
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.