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b and c goes to question 1 PLEASE ANSWER ALL Suppose that I construct a confidence...

b and c goes to question 1 PLEASE ANSWER ALL

  1. Suppose that I construct a confidence interval for the mean test grade on paper 1 using Statcrunch and get Upper Limit, 68.9 and a lower limit 76.3. State the conclusion for the confidence interval.
  2. b)What happens to the confidence interval as we increase the sample size? Explain your reasoning (explanations without reasoning will not be given credit.)
  3. c)When should we use the t-distribution instead of the z-distribution?
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Answer #1

b. The margin of error for confidence interval of mean is . The width of the confidence interval is twice the margin of error. n is the Sample size. So clearly if we increase the sample size then the margin of error will decrease. And also the width of the confidence interval will decrease.

So if we increase sample size the width of the confidence interval will decrease.

c. We should use t distribution when we don't know about the population standard deviation . Then we estimate the population standard deviation by sample standard deviation and use t distribution instead of z distribution to find the critical value.

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