HW 8
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University of New Mexico, Main Campus *
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Course
1350
Subject
Mathematics
Date
Jan 9, 2024
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docx
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2
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[Last Name] 1
Alysandra Dominguez
MATH1350
HOMEWORK 8
1.
The researcher's prediction is false is the null hypothesis. The possibility that the difference the
researcher projected is real is the alternate hypothesis. Thus, we may choose between a null
hypothesis and an alternative native hypothesis using the two-sample t-test. In order to test the
zero-degree significant difference, the null hypothesis was used. The null hypothesis could
occasionally be incorrect. Once it is rejected, we may accept the alternative hypothesis;
otherwise, the test would encounter two different types of errors while testing the hypothesis.
Rejecting a genuine null hypothesis is known as a type I error in statistical hypothesis testing, but
failing to reject a false null hypothesis is known as a type lI error.
2.
The correlations between variables of real-world applications are known as practical importance.
The likelihood that two or more variables will have a link is indicated by a statistical significance.
It considers both means and variance. For the variables to have practical value, statistical
significance is not a must. In certain instances, the two meanings could be reliant on one another.
3.
Calculating the one-sample t-test's t.05: For the one-sample t-test, the degrees of freedom (df) are
equal to N-1, where N is the sample size. The obtained df's t.05 value may be found in the t-
tables.025 column. Calculating the matched-pairs t-test's t.05: For the one-sample t-test, the
degrees of freedom (df) are equal to N-1, where N is the number of score pairings (or subjects).
The obtained df's t.05 value may be found in the t-tables.025 column.
4.
A. The biofeedback training, which is offered at two different levels—before and after the
seminar—serves as the study's independent variable. The goal of the experiment is to see how this
variable influences the total number of headaches.
The number of headaches the respondents reported is the dependent variable. Since the variation
in headache counts may be measured, it is measured using an interval scale.
B. The number of headaches before and after the biofeedback training seminar is the same,
according to the null hypothesis. The alternate hypothesis claims that muscular relaxation causes
a drop in headache frequency following the seminar.
C.
t-Test: Paired Two Sample for Means
Before Seminar
After Seminar
Mean
8.555555556
2.888888889
Variance
16.77777778
5.111111111
Observations
9
9
Pearson Correlation
0.250471949
Hypothesized Mean Difference
0
df
8
t Stat
4.093119005
P(T<=t) one-tail
0.001735299
t Critical one-tail
1.859548038
P(T<=t) two-tail
0.003470598
t Critical two-tail
2.306004135
Since tobt (8) = 4.09, p < .01; Reject the null
hypothesis
D. The average difference in the number of reported severe headaches seems to point to a
meaningful benefit of biofeedback training in lowering the frequency of severe headaches rather
than just random error and chance.
[Last Name] 2
E. Part C may have a Type I statistical mistake, which is the wrong rejection of the null
hypothesis, leading to the appearance of a substantial difference in the number of headaches when
there is none.
F.
Type 1 error: falsely rejection of a null hypothesis that is true.
G.
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