STA 1060 Chapter 6 Examples
1. An estimate is needed for the mean airfare price (in dollars) for a one-way ticket from Atlanta
to Chicago. A random sample of 35 prices is selected and the average is found to be $101.77
with a standard deviation of $6.69.
a. Find a point estimate for the population mean .
b. Find the maximum error of the estimate for the mean airfare with a 95% level of
confidence.
c. Find a 95% confidence interval for the mean one-way fare from Atlanta to Chicago.
Interpret the interval found.
2. If you want to estimate the mean one-way fare from Atlanta to Chicago to within $2 of the
population mean with 95% confidence, how many fares must you sample?
3. In a random sample of 13 Downtown Orlando residents, the mean mileage to work was 4.3
miles and the standard deviation was 0.3 miles. Assume the variable is normally distributed
and construct a 90% confidence interval for the mean of the population. Interpret the interval
found.
4. In a study of 1907 teenagers (picked at random) 449 had acne problems. Construct a 95%
confidence interval for the proportion of teenagers with acne problems. Interpret the interval
found.
5. Suppose you want to estimate the proportion of people that wear seat belts in Florida. If you
need the estimate to be within 2% of the true proportion with 99% confidence, how many
people do you need to sample?
Chapter 6
problem#1
problem#4
Population Standard
Deviation
Sample Mean
Sample Size
Confidence Level
Standard Error of the Mean
6.69
101.77
35
95%
1.130816393
Z Value
Interval Half Width
Interval Lower Limit
Interval Upper Limit
-1.95996279
2.216358049
99.55364195
103.986358
problem#2
Population Standard
Deviation
Sampling Error
Confidence Level
Z Value
Calculated Sample Size
Sample Size Needed
1907
449
95%
0.23544835
-1.95996279
0.00971574
0.01904249
0.21640586
0.25449084
problem#5
6.69
2
95%
-1.95996279
42.98212627
43
Problem#3
Sample Standard Deviation
Sample Mean
Sample Size
Confidence Level
Standard Error of the Mean
Degrees of Freedom
t Value
Interval Half Width
Interval Lower Limit
Interval Upper Limit
Sample Size
Number of Successes
Confidence Level
Sample Proportion
Z Value
Standard Error of the
Proportion
Interval Half Width
Interval Lower Limit
Interval Upper Limit
0.3
4.3
13
90%
0.083205029
12
1.782286745
0.148295221
4.15
4.45
Estimate of True Proportion
Sampling Error
Confidence Level
Z Value
Calculated Sample Size
Sample Size Needed
0.5
0.02
99%
-2.57583134
4146.81693
4147