Statistics 5021 – Homework 5
There are 20 total points (0.5 points for each part of each question and 8 points for handing
in the assignment).
One question will be graded for correctness.
This homework is due
Thursday, March 24 in your lab section.
1. James is conducting a hypothesis test for
μ
, the mean of the distribution of heights,
H
0
:
μ
= 65 inches
H
a
:
μ
6
= 65 inches
He develops a decision rule where he will fail to reject
H
0
if ¯
x
, the observed sample
mean height, is between 64 and 66 inches, otherwise he will reject. Notice that he is
ignoring the sample size and observed sample standard deviation.
(a) Compute the probability of a type I error of James’ decision rule if it were to be
conducted with a random sample of size
n
= 100 from
N
(
μ
= 65
, σ
= 4)
(b) Compute the probability of a type II error of James’ decision rule if it were to be
conducted with a random sample of size
n
= 100 from
N
(
μ
= 66
, σ
= 4)
2. The data are 35 measured systolic blood pressures in mmHg
159
92 102
92
90
91
96
91 118 136
91
90 111
92
90
91
90 151
92
90 146
94
90
90
91
90 176
95
90
90 159
92 109
90 106
The observed sample mean is ¯
x
= 104
.
6571 mmHg and the observed sample standard
deviation is
s
= 24
.
53082 mmHg. A researcher feels that using the Normal distribution
to model systolic blood pressures for the population is problematic. Is there statistical
evidence at the
α
= 5% level that
μ
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 Spring '08
 Staff
 Statistics, Standard Deviation, Null hypothesis, Statistical hypothesis testing

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