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# Interpretation of Type I and Type II Errors in Hypothesis Testing

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Dr. Jeffrey M. Barrett of Lakeland, Florida, reported data on eight cases of
umbilical cord prolapse. The maternal ages were 25, 28, 17, 26, 27, 22, 25, and 30.
He was interested in determining if he could conclude that the mean age of the
population of his sample was greater than 20 years. Let x = .01.

The null and alternative hypotheses for this problem are defined as:
H0 : μ=20 and Ha : μ>20

a. explain the meaning of a type I error in the context of this problem
b. explain th meaning of a Type II error in the context of this problem.
c. suppose dr barrett expanded his study to include a total of 50 subjects and then calculated a test statistic or z=2.33 for his hypothesis test. what is the associated p-value? what is the conclusion for this test?

https://brainmass.com/statistics/frequentist-inference/571540

#### Solution Preview

Inferential Statistics
Dr. Jeffrey M. Barrett of Lakeland, Florida, reported data on eight cases of
umbilical cord prolapse. The maternal ages were 25, 28, 17, 26, 27, 22, 25, and 30.
He was interested in determining if he could conclude that the mean age of the
population of his sample was greater than 20 years. Let x = .01. (I'm assuming that this means that alpha = 0.01?)
The null and alternative hypotheses for this problem are defined as:
H0 : μ=20 and Ha : μ>20
a. explain the meaning of a type I error in the context of this problem
A Type I Error is said to occur in a hypothesis test whenever the null hypothesis is actually true (which means that the alternative hypothesis must be false), but the data collected leads you to reject the null hypothesis, which leads you to believe what the alternative hypothesis says.
In the context of his problem, if a type I error were to occur, then that would mean that in reality the ...

#### Solution Summary

Type I and Type II errors are defined, and the meaning of making a type I error or a type II error in a hypothesis test is interpreted within the context of the specific hypothesis test being conducted. Also, the p-value approach to deciding whether to reject or fail to reject the null hypothesis is explored and explained with an example.

\$2.19

## Statistics: Type I and Type II Error Analysis

The dataset for this case is included in the Excel spreadsheet uploaded to OLS
Payment
27
24
14
39
13
31
26
33
13
23
17
24
18
34
13
23
16
32
30
29
21
19
22
14
27
20
11
20
30
24
18
21
24
18
27
27
27
21
22
23
18
17
23
26
20
20
22
21
13
36
18
25
26
19
16
28
16
20
16
14
25
14
35
17
16
19
19
17
18
22
23
22
27
23
23
21
20
18
29
32
27
15
21
26
32
20
29
25
15
21
30
24
23
14
18
22
37
24
35
29
24
17
27
15
19
12
19
21
19
21
15
17
20
21
31
19
27
19
26
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26
23
12
20
34
21
24
20
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16
23
13
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31
29
23
28
19
19
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14
25
17
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21
18
22
15
27
14
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30
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17
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24
17
10
25
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13
29
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11
25
30
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26
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15
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28
27
22
12
25
12
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16
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30
16
25
13
11
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28
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19
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31
9
14
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28

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