Statistics 104 – Laboratory 11
Inference for a population mean, μ , when σ is not known.
1. In a study of youths in the East Boston area, several different measurements were
made on girls age 5 to 17. Below are the heights (inches) of 24 randomly selected
girls from East Boston.
60.0 52.0 59.0 64.0 54.0 61.5 56.5 62.5 64.5 59.0 57.5 68.0
63.0 64.5 62.0 62.0 71.0 64.5 63.5 68.0 65.0 60.0 67.5 70.0
n = 24 , y = 62.48, s = 4.74
a) Construct a 95% confidence interval for the mean height of all girls in
East Boston age 5 to 17.
b) Give an interpretation of this confidence interval.
c) Is 60 inches a plausible value for the mean height of girls age 5 to 17 in
East Boston? Support your answer by referring to the confidence interval
you constructed in b).
2. The local grocery store packages different grades (based on fat content) of
hamburger. Usually the leaner (less fat) grades are more expensive. A simple
random sample of 12 one-pound packages of hamburger is obtained from the
local store and tested for fat content. Below are the percentages of lean meat for
each package.
90.9
94.3
91.9
92.5
91.8 93.4
91.6
92.6
92.3
93.6
93.1
93.2
a) Calculate the sample mean percentage of lean meat and the sample
standard deviation.
b) The packages are labeled 93% lean. Use the summaries in a) to test the
hypothesis H0: μ = 93 against HA: μ < 93, where μ is the population mean
percentage lean. Be sure to calculate the appropriate test statistic and Pvalue, reach a decision and justify that decision, and state a conclusion.
c) Based on the test in b), are the packages labeled correctly? Explain
briefly.
3. Attached is JMP output for the analysis of body temperature (oF) for 65 randomly
selected females.
a) Give the 90% confidence interval for the population mean body
temperature for females.
b) Test the hypothesis that the population mean body temperature for females
is 98.6 oF against the alternative that the population mean body
temperatures for females is less than 98.6 oF. Be sure to include all steps
for the test of hypothesis.
1
Distribution: Body Temperature for Females
Normal Quantile Plot
3
.99
2
.95
.90
1
.75
0
.50
.25
-1
.10
.05
-2
.01
-3
15
10
Count
20
5
97
98
99
100
101
Quantiles
100.0%
75.0%
50.0%
25.0%
0.0%
Moments
maximum
quartile
median
quartile
minimum
100.80
98.80
98.40
98.00
96.40
Mean
Std Dev
Std Err Mean
upper 95% Mean
lower 95% Mean
N
98.393846
0.7434878
0.0922183
98.578073
98.209619
65
Confidence Intervals
Parameter
Mean
Estimate
98.39385
Lower CI
98.23993
Upper CI
98.54776
1-Alpha
0.900
Test Mean=value
Hypothesized Value
Actual Estimate
df
Std Dev
98.6
98.3938
64
0.74349
Test Statistic
Prob > |t|
Prob > t
Prob < t
t Test
-2.2355
0.0289
0.9856
0.0144
2
Statistics 104 – Laboratory 11
Group Answer Sheet
Names of Group Members:
____________________, ____________________
____________________, ____________________
1. In a study of youths in the East Boston area, several different measurements were
made on girls age 5 to 17. Below are the heights (inches) of 24 randomly selected
girls from East Boston.
60.0 52.0 59.0 64.0 54.0 61.5 56.5 62.5 64.5 59.0 57.5 68.0
63.0 64.5 62.0 62.0 71.0 64.5 63.5 68.0 65.0 60.0 67.5 70.0
n = 24 , y = 62.48, s = 4.74
a. Construct a 95% confidence interval for the mean height of all girls in
East Boston age 5 to 17.
b. Give an interpretation of this confidence interval.
c. Is 60 inches a plausible value for the mean height of girls age 5 to 17 in
East Boston? Support your answer by referring to the confidence interval
you constructed in b).
3
2. The local grocery store packages different grades (based on fat content) of
hamburger. Usually the leaner (less fat) grades are more expensive. A simple
random sample of 12 one-pound packages of hamburger is obtained from the
local store and tested for fat content. Below are the percentages of lean meat for
each package.
90.9
94.3
91.9
92.5
91.8 93.4
91.6
92.6
92.3
93.6
93.1
93.2
a. Calculate the sample mean percentage of lean meat and the sample
standard deviation.
b. The packages are labeled 93% lean. Use the summaries in a) to test the
hypothesis H0: μ = 93 against HA: μ < 93, where μ is the population mean
percentage lean. Be sure to calculate the appropriate test statistic and Pvalue, reach a decision and justify that decision, and state a conclusion.
c. Based on the test in b), are the packages labeled correctly? Explain
briefly.
4
3. Attached is JMP output for the analysis of body temperature (oF) for 65 randomly
selected females.
a. Give the 90% confidence interval for the population mean body
temperature for females.
b. Test the hypothesis that the population mean body temperature for females
is 98.6 oF against the alternative that the population mean body
temperatures for females is less than 98.6 oF. Be sure to include all steps
for the test of hypothesis.
5