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CHAPTER PROBLEMS: HYPOTHESIS TESTING
10 questions, 30 points
Chapter 7
Multiple Choice
1. A researcher suspects that the actual prevalence of generalized anxiety among children and
adolescents is higher than the previously reported prevalence of generalized anxiety disorder
among children and adolescents. The previously reported prevalence of generalized anxiety
disorder among children and adolescents is 4.1%, and the researcher conducts a study to test the
accuracy of the previously reported prevalence of generalized anxiety disorder by recruiting 98
children and adolescents from various pediatricians’ offices and tests them for generalized
anxiety disorder using the DSM-5. The researcher determines that the prevalence of generalized
anxiety disorder among the participants of the study is 6.8%. The researcher’s hypothesis, for a
level of significance of 5%, should resemble which of the following sets of hypothesis?
a. H0: p > .041; H1: p = .041; alpha= .05
b. H0: p > .041; H1: p = .041; alpha= .95
c. H0: p = .041; H1: p > .041; alpha= .05
d. H0: p = .041; H1: p > .041; alpha= .95
2. A researcher suspects that the actual prevalence of generalized anxiety among children and
adolescents is higher than the previously reported prevalence of generalized anxiety disorder
among children and adolescents. The previously reported prevalence of generalized anxiety
disorder among children and adolescents is 4.1%, and the researcher conducts a study to test the
accuracy of the previously reported prevalence of generalized anxiety disorder by recruiting 98
children and adolescents from various pediatricians’ offices and tests them for generalized
anxiety disorder using the DSM-5. The researcher determines that the prevalence of generalized
anxiety disorder among the participants of the study is 6.8%. Calculate the z value for the test
statistic.
a. z = 1.12
b. z = 1.09
c. z = 43.56
d. z = 1.35
3. A researcher suspects that the actual prevalence of generalized anxiety among children and
adolescents is higher than the previously reported prevalence of generalized anxiety disorder
among children and adolescents. The previously reported prevalence of generalized anxiety
disorder among children and adolescents is 4.1%, and the researcher conducts a study to test the
accuracy of the previously reported prevalence of generalized anxiety disorder by recruiting 98
children and adolescents from various pediatricians’ offices and tests them for generalized
anxiety disorder using the DSM-5. The researcher determines that the prevalence of generalized
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anxiety disorder among the participants of the study is 6.8%. For a level of significance of 5%,
what should the researcher’s decision rule look like?
a. Reject H0 if z is less than or equal to -1.96.
b. Reject H0 if z is greater than or equal to 1.96.
c. Reject H0 if z is less than or equal to -1.645.
d. Reject H0 if z is greater than or equal to 1.645.
4. A researcher suspects that the actual prevalence of generalized anxiety among children and
adolescents is higher than the previously reported prevalence of generalized anxiety disorder
among children and adolescents. The previously reported prevalence of generalized anxiety
disorder among children and adolescents is 4.1%, and the researcher conducts a study to test the
accuracy of the previously reported prevalence of generalized anxiety disorder by recruiting 98
children and adolescents from various pediatricians’ offices and tests them for generalized
anxiety disorder using the DSM-5. The researcher determines that the prevalence of generalized
anxiety disorder among the participants of the study is 6.8%. What should the researcher’s
conclusion be for a 5% significance level?
a. We reject H0 at the 5% level because 1.35 is less than -1.96. We do have statistically
significant evidence to show the actual prevalence of generalized anxiety disorder among
children and adolescents is above the previously reported prevalence of 4.1%.
b. We fail to reject H0 at the 5% because 1.35 is less than 1.645. We do not have statistically
significant evidence to show the actual prevalence of generalized anxiety disorder among
children and adolescents is above the previously reported prevalence of 4.1%.
c. We fail to reject H0 at the 5% because 1.09 is less than 1.96. We do not have statistically
significant evidence to show the actual prevalence of generalized anxiety disorder among
children and adolescents is above the previously reported prevalence of 4.1%.
d. We fail to reject H0 at the 5% because 43.56 is greater than 1.645. We do not have
statistically significant evidence to show the actual prevalence of generalized anxiety
disorder among children and adolescents is above the previously reported prevalence of
4.1%.
5. A new drug to treat psoriasis has been developed and is in clinical testing. Assume that those
individuals given the drug are examined before receiving the treatment and then again after
receiving the treatment to determine if there was a change in their symptom status. If the initial
results showed that 9.0% of individuals entered the study in remission, 74.0% of individuals
entered the study with mild symptoms, 13.0% of individuals entered the study with moderate
symptoms, and 4.0% entered the study with severe symptoms calculate and interpret a chi-
squared test to determine if the drug was effective treating psoriasis given the information below
from the final examination.
Remission
(No
Symptoms of
Psoriasis)
Mild
Symptoms
of Psoriasis
Moderate
Symptoms
of Psoriasis
Severe
Symptoms of
Psoriasis
Total
Number of
Participants
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to Receive
the Drug
Number of
Participants
455
635
85
7
1182
a. We reject H0 because 1273.142 is greater than 5.99. We have statistically significant
evidence at the alpha equals .05 level to show that the distribution of the severity of
psoriasis cases at the end of the clinical trial for the sample is different from the
distribution of the severity of psoriasis cases prior to the administration of the drug,
suggesting the drug is effective.
b. We reject H0 because 1273.142 is greater than 9.51. We have statistically significant
evidence at the alpha equals .05 level to show that the distribution of the severity of
psoriasis cases at the end of the clinical trial for the sample is different from the
distribution of the severity of psoriasis cases prior to the administration of the drug,
suggesting the drug is effective.
c. We reject H0 because 1273.142 is greater than 7.81. We have statistically significant
evidence at the alpha equals .05 level to show that the distribution of the severity of
psoriasis cases at the end of the clinical trial for the sample is different from the
distribution of the severity of psoriasis cases prior to the administration of the drug,
suggesting the drug is effective.
d. We reject H0 because 1273.142 is greater than 11.07. We have statistically significant
evidence at the alpha equals .05 level to show that the distribution of the severity of
psoriasis cases at the end of the clinical trial for the sample is different from the
distribution of the severity of psoriasis cases prior to the administration of the drug,
suggesting the drug is effective.
True/False
6. True or False? For a two-tailed test using z values at the 5% significance level we reject H0 if z
≤ -1.960 or if z ≥ 1.960
7. True or False? Assume a researcher recruits 150 African American and Caucasian individuals
taking warfarin to determine if there is a difference in the mean dosage of the medication needed
to cause a decrease in their INR blood test. If the mean dosage for 75 Caucasian individuals
required to get their INR blood test in range is 6.1 mg with a standard deviation of 1.7 mg and
the mean dosage for 75 African American individuals required to get their INR blood test in
range is 4.3 mg with a standard deviation of 0.9 mg, the Sp value obtained while calculating the
test statistic is approximately 1.10 mg.
8. True or False? Assume a researcher recruits 150 African American and Caucasian individuals
taking warfarin to determine if there is a difference in the mean dosage of the medication needed
to cause a decrease in their INR blood test. If the mean dosage for 75 Caucasian individuals
required to get their INR blood test in range is 6.1 mg with a standard deviation of 1.7 mg and
the mean dosage for 75 African American individuals required to get their INR blood test in
range is 4.3 mg with a standard deviation of 0.9 mg, the z value obtained while calculating the
test statistic is approximately 9.60.
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9. True or False? Assume a researcher recruits 150 African American and Caucasian individuals
taking warfarin to determine if there is a difference in the mean dosage of the medication. If the
mean dosage for 75 Caucasian individuals required to get their INR blood test in range is 6.1 mg
with a standard deviation of 1.7 mg and the mean dosage for 75 African American individuals
required to get their INR blood test in range is 4.3 mg with a standard deviation of 0.9 mg, the
decision rule for a 10% level of significance would be to reject H0 if z ≤ -1.645 or z ≥ 1.645
10. True or False? H0 for an ANOVA test often states that all the mean values from the different
independent samples are not equal.
