5.4 A random sample of 90 observations produced a mean 25.9
and a standard deviation s=2.7
a. Find an approximate 95% confidence interval for the
population mean m
b. Find an approximate 90% confidence interval
c. Find an approximate 99% confidence interval
5.8 The mean and standard deviation of a random sample of n
measurements are equal to 33.9 and 3.3, respectively.
a. Find a 95% confidence interval for m if n= 100
b. Find a 95% confidence interval for m if n =400
c. Find the widths of the confidence intervals found in
parts a and b.What is the effect on the width of a confidence interval of quadrupling the sample size while
holding the confidence coefficient fixed?
5.25 The following random sample was selected from a normal
distribution: 4, 6, 3, 5, 9, 3.
a. Construct a 90% confidence interval for the population
mean m 5 +- 1.88
b. Construct a 95% confidence interval for the population
mean m 5+- 2.39
c. Construct a 99% confidence interval for the population
mean m 5+- 3.75
d. Assume that the sample mean and sample standard
deviation s remain exactly the same as those you just
calculated but are based on a sample of n=25 observations
rather than n=6 observations. Repeat
parts a–c. What is the effect of increasing the sample
size on the width of the confidence intervals? a)5+- 78.5+-94.5+-1.28 b) the sample size of the width will decrease
5.37 For the binomial sample information summarized in each
part, indicate whether the sample size is large enough to
use the methods of this chapter to construct a confidence
interval for p.
a n= 400 p =.10 Yes b.n= 50 p = .10 NO
c. n=20 Yes and No d.n=20 p = .3 NO
5.41 Is Starbucks coffee overpriced?The Minneapolis Star Tribune (August 12, 2008) reported that 73% of Americans say that
Starbucks coffee is overpriced.The source of this information was a national telephone survey of 1,000 American adults
conducted by Rasmussen Reports.
Identify the population of...
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