A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x overbar, is found
to be 109, and the sample standard deviation, s, is found to be 10. (a) Construct a 96% confidence interval about mu if the sample size, n, is 29. (b) Construct a 96% confidence interval about mu if the sample size, n, is 25. (c) Construct a 90% confidence interval about mu if the sample size, n, is 29. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed? LOADING... Click the icon to view the table of areas under the t-distribution.
2 answers:
Answer:
a: 105.2 < µ < 112.8
b: 104.872 < µ < 113.128
c: 105.841 < µ < 112.159
d: No, because n < 30
Step-by-step explanation:
For a - c, see attached photos for work. There are 2 formulas to use. The steps for constructing any confidence interval are the same, you will just use different numbers in the formula depending on what data is given to you.
d: With large sample sizes, the data often resembles normally distributed data, so we can still construct confidence intervals from the data.
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