Question

Constructing Confidence Intervals In Exercises 17 and 18, you are given the sample mean and the sample standard deviation. Assume the variable is normally distributed and use a normal distribution or a t-distribution to construct a 90% confidence interval for the population mean u. If convenient, use technology to construct the confidence intervals.

(a) In a random sample of 10 adults from the United States, the mean waste generated per person per day was 4.54 pounds and the standard deviation was 1.21 pounds. (b) Repeat part (a), assuming the same statistics came from a sample size of 500. Compare the results. (Adapted from U.S. Environmental Protection Agency)

answer

a

b

Answer 1

a) (3.839 , 5.241)

b)  (4.451 , 4.629)

width of confidence interval for part a) is larger than width of confidence

inteval iin part b)

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C=90%

a) n= 10, = 4.54, s= 1.21

formula for confidence interval is

Where tc is the t critical value for c=90% with df= n-1 = 9

We get

tc= 1.833

4.54−0.701 < < 4.54+0.701

(3.839 , 5.241)

We get confidence interval as (3.839 , 5.241)

b)

n= 500, = 4.54,

sample size is large hence we can assume sample standard deviation as population standard deviation ( ) hence,

= 1.21

formula for confidence interval is

Where tc is the Z critical value for c=90%

We get

tc= 1.645

4.451 < < 4.629

We get confidence interval as (4.451 , 4.629)