STA 2023
Section 6.1
Confidence Intervals for the
Mean (Large Samples)
Estimating Population Parameters

Critical Values


Margin of Error

 Example
2: A random sample of 120 students has a
test score average with a standard deviation of 9.2.
Find the margin of error if c = 0.98.

Answer: 1.96
 Example
3: A random sample of 40 students has a
mean annual earnings of $3120 and a standard
deviation of $677. Find the margin of error if c =
0.95.

Answer: $210
Confidence Intervals for the Population Mean


Example 4: A random sample of 150 students has a grade point
average with a mean of 2.86 and with a standard deviation of
0.78. Construct the confidence interval for the population mean,
μ, if c = 0.98.
 Answer: (2.71, 3.01)
 Interpretation: We are 98% confident that the population
grade point average is between 2.71 and 3.01.

Example 5: In a sample of 10 randomly selected women, it was
found that their mean height was 63.4 inches. From previous
studies, it is assumed that the standard deviation σ is 2.4 and
that the population of height measurements is normally
distributed. Construct the 95% confidence interval for the
population mean.
 Answer: (61.9, 64.9)
 Interpretation: With 95% confidence, the average height of all
women is between, 61.9 inches and 64.9 inches.
 Example
6: The number of wins in a season for 32
randomly selected professional football teams are
listed below. Construct a 90% confidence interval
for the true mean number of wins in a season.
9
11
12
12
9
10
10
9
 Answer:
9
6
7
9
(7.2, 8.8)
8
4
5
7
10
11
12
10
9
9
6
7
7
8
4
7
2
8
3
5
Minimum Sample Size.
