Mind On Statistics - Chapter 13 Worksheets With Answers Page 7
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32Chapter 13
33.
Explain the difference between the null and alternative hypotheses in hypothesis testing. Give an example.
KEY: The typical null hypothesis specifies a specific value for a population parameter; the alternative hypothesis
specifies a range of values. The null hypothesis describes the status quo, or the condition of no difference in a
paired design. The alternative hypothesis describes a change, or the condition of a difference in a paired
design. For testing about the value of a population mean
, a null hypothesis could be H
:
= 10 and the
0
alternative hypothesis could be H
:
10.
a
Questions 34 to 37: A sample of n = 9 men are asked. "What's the fastest you've ever driven a car?" The sample
mean is 120 mph and the standard deviation is 30.
34.
What is the value of the t-test statistic for testing the null hypothesis that the population mean response is 100
mph?
KEY: The value of the t-test statistic is 2.00.
35.
What are the degrees of freedom for conducting this t-test?
KEY: The degrees of freedom are n – 1 = 9 – 1 = 8.
36.
Find the p-value for testing whether the population mean response is more than 100 mph?
KEY: The corresponding p-value = 0.040.
37.
Give an appropriate conclusion using a 1% level of significance.
KEY: The results are not statistically significant so the null hypothesis cannot be rejected. There is not enough
evidence to conclude that the population mean is more than 100 mph.
Questions 38 to 40: A group of women suffering from various types of obsessive fear is given a therapeutic course
to learn how to handle their fear. At the beginning of the course the women are given a questionnaire to determine
how afraid they are. Fear scores range between 100 and 400. SPSS is used to obtain descriptive statistics. Output is
shown below.
The course coordinator wishes to test if the women score significantly lower than 250.
38.
What is the value of the t-test statistic?
KEY: t = −0.214
39.
What do we know about the p-value for this test?
KEY: p-value > 0.10 (p-value = 0.416)
40.
Give an appropriate conclusion using a 10% level of significance.
KEY: The results are not statistically significant. There is not enough evidence to conclude that the population mean
fear score is lower than 250.
267
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