Statistics 104 – Laboratory 10
Inference for a population mean, μ .
In laboratory 9 we looked at the distribution of the sample mean y by sampling from a
population of 250 females who took an introductory statistics class. In this lab we look at
inference for the population mean height for the population of 250 females.
1. Below is a histogram of the population of 250 female heights.
0.05
0.03
Density
0.04
0.02
0.01
140
150
160
170
180
190
Height (cm)
Describe the shape of the distribution. Why is it reasonable to use a normal model for
this population?
2. You will use the sample data your group collected in laboratory 9 for this lab. Your
instructor will give you a copy of your group answer sheet from that lab. Recall that your
population standard deviation is σ = 7.6 cm .
a) For each of your group’s 4 samples of size n = 10 construct an 80% confidence
interval for the population mean μ .
b) How many of the 4 confidence intervals you constructed actually contain the
population mean of 166.6 cm? Put this information on the blackboard.
c) How many of the confidence intervals for the whole lab section actually contain the
population mean of 166.6 cm?
d) Theoretically, what percentage of 80% confidence intervals, n = 10 , will contain the
population mean of 166.6 cm?
e) Will a 95% confidence interval be narrower than, the same width as or wider than an
80% confidence interval, n = 10 ? Explain briefly.
f) Will a 95% confidence interval based on n = 10 values be narrower than, the same
width as or wider than a 95% confidence interval based on n = 40 values? Explain
briefly.
g) Construct a 95% confidence interval for combined sample of n = 40 .
h) Theoretically, what percentage of 95% confidence intervals n = 40 , will contain the
population mean of 166.6 cm?
3. Use your combined sample of size 40 to test the hypothesis that the population mean
height is 166.6 cm against the alternative that the population mean height is not 166.6 cm.
Include a step-by-step procedure to test the hypothesis with σ = 7.6 cm and α = 0.05 .
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Stat 104 – Laboratory 10
Group Answer Sheet
Names of Group Members:
____________________, ____________________
____________________, ____________________
1. Describe the shape of the distribution. Why is it reasonable to use a normal model for
this population?
2.
a) For each of your group’s 4 samples of size n = 10 construct an 80% confidence
interval for the population mean μ .
Sample 1:
Sample 2:
Sample 3:
Sample 4:
b) How many of the 4 confidence intervals you constructed actually contain the
population mean of 166.6 cm?
c) How many of the confidence intervals for the whole lab section actually contain the
population mean of 166.6 cm?
d) Theoretically, what percentage of 80% confidence intervals, n = 10 , will contain the
population mean μ ?
2
e) Will a 95% confidence interval be narrower than, the same width as or wider than an
80% confidence interval, n = 10 ? Explain briefly.
f) Will a 95% confidence interval based on n = 10 values be narrower than, the same
width as or wider than a 95% confidence interval based on n = 40 values? Explain
briefly.
g) Construct a 95% confidence interval for combined sample of n = 40 .
h) Theoretically, what percentage of 95% confidence intervals n = 40 , will contain the
population mean μ ?
3. Use your combined sample of size 40 to test the hypothesis that the population mean
height is 166.6 cm against the alternative that the population mean height is not 166.6 cm.
Include a step-by-step procedure to test the hypothesis with α = 0.05 .
3