A simple tandem sample of size n is dawn from a population that is normally dist

Question

A simple tandem sample of size n is dawn from a population that is normally distributed. The sample mean, x is found to be 111, and the sample standard deviation, s is found to be 10. (a) Construct an 80% confidence interval about mu if the sample size, n is 27. (b) Construct an 80% confidence interval about mu if the sample size, n is 20. (c) Construct a 70% confidence interval about mu if the sample size, n is 27. (d) Could we have the confidence intervals in parts (a) - (c) if the population had not been normally distributed? (a) Construct an 80% confidence interval about mu if the sample size, n is27. Lower bound Upper bound (Use ascending order Round to one decimal place as needed.)

Explanation / Answer

The statistical software outputs for this problem are:

One sample T confidence interval:
: Mean of population

80% confidence interval results:

80% confidence interval results:

70% confidence interval results:

Hence,

a) Lower bound = 108.5

Upper bound = 113.5

b) Lower bound = 108.0

Upper bound = 114.0

c) Lower bound = 109.0

Upper bound = 113.0

d) No, because the sample sizes are less than 30.

Mean Sample Mean Std. Err. DF L. Limit U. Limit 111 1.9245009 26 108.46934 113.53066

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