Statistics Question

PM 510 Homework 3
Problems not marked with [SPSS] should be done by hand, as problems similar to those could be
on the Midterm and/or Final. (Of course, feel free to check your work using SPSS!)
Problems marked with [SPSS] are intended to be done with SPSS. For these problems, please
attach the output file.
1. If a one-sided, one-sample t-test indicates that the null hypothesis can be rejected at the α = 0.05
level of significance, then which of the following statements are true? (For each, explain why.)
(a) The one-sided test will definitely be significant at the α = 0.01 level of significance.
(b) The one-sided test will definitely be significant at the α = 0.10 level of significance.
(c) The one-sided test cannot be significant at the α = 0.01 level of significance.
(d) A two-sided test on the same set of data will definitely be significant at the α = 0.05 level of
significance.
(e) A two-sided test on the same set of data will definitely be significant at the α = 0.10 level of
significance.
(f) A two-sided test on the same set of data might not be significant at the α = 0.05 level of
significance.
2. [SPSS] Use SPSS (you can use a blank dataset or any open dataset) to calculate the following
probabilities. Provide the answers to each question, as well as a screenshot of your data viewer
showing all the newly created variables.
Consider the t-distribution with 8 degrees of freedom.
(a) What proportion of the area under the curve lies to the right of t = 1.397?
(b) What proportion of the area under the curve lies to the left of t = –2.306?
(c) What proportion of the area under the curve lies between t = –3.355 and t = 3.355?
(d) What value of t cuts off the lower 2.5% of the distribution?
3. The distribution of diastolic blood pressure for the population of female diabetes patients or patients
with diabetes between the ages of 30 and 34 has an unknown population mean μbp, but a known
population standard deviation of σbp = 9.1 mm Hg. It may be useful for physicians to know whether
the mean of this population is equal to the mean diastolic blood pressure of the general population
of females in this age group, which is 74.4 mm Hg. A random sample of 15 diabetic women is selected;
their average diastolic blood pressure is bp = 82 mm Hg. Using this information, conduct a two-sided
test at the α = 0.05 level of significance.
(a) Identify the Dependent variable and variable type (if categorical, define the levels of the variable)
(b) Identify the Independent variable and variable type (if categorical, define the levels of the
variable, if none, state that)
(c) What type of test should you perform? Why?
(d) What are the null and alternative hypotheses of the appropriate test? Be sure to define the
population parameter of interest.
(e) What is the p-value for the test?
(f) What conclusion do you draw from the result of the test? Describe your conclusion as if you were
writing a scientific article.
(g) Would your conclusion have been different if you had chosen α = 0.01 instead of α = 0.05?
4. Researchers examined anxiety and depression in COVID-19 survivors. A total of 96 subjects that had
previously been diagnosed were administered the Zung Self-rating Depression Scale (SDS). The SDS
test asks 20 questions and assigns a score. The total of these scores is then calculated by summing the
scores and multiplying by 1.25. The higher the score, the more depressive the symptoms. The mean
SDS score among these subjects was 40.2 with a standard deviation of 11.40. In the general
population of the US, the mean SDS score is 34.9. Assume that the population variance is unknown.
The researchers wanted to test if the sample of COVID-19 survivors were more depressed than the
general population.
(a) Identify the Dependent variable and variable type (if categorical, define the levels of the variable)
(b) Identify the Independent variable and variable type (if categorical, define the levels of the
variable, if none, state that)
(c) What type of test should you perform? Why?
(d) What are the null and alternative hypotheses? Be sure to define the population parameter of
interest.
(e) Conduct the test at the α = 0.05 level.
(f) Describe your conclusions.
5. [SPSS] The declared concentrations of tar (in mg/cigarette) for 35 brands of Canadian cigarettes are
saved under the variable name tar in the file cigarett.sav. In the European Union (EU), the maximum
amount of tar allowed per cigarette is 10 mg. Suppose that a Canadian exporter wants to test whether
an average cigarette brand from Canada would be legal to export to the EU. Assume that the 35
brands were randomly sampled from all possible brands of cigarettes in Canada.
(a) Identify the Dependent variable and variable type (if categorical, define the levels of the variable)
(b) Identify the Independent variable and variable type (if categorical, define the levels of the
variable, if none, state that)
(c) What type of test should you perform? Why?
(d) What are the null and alternative hypotheses? Be sure to define the population parameter of
interest.
(e) Conduct an appropriate hypothesis test at the α = 0.05 level of significance. Attach the SPSS
output. What is the p-value for the test?
(f) What conclusion do you draw from the result of the test? Describe your conclusion as if you were
writing a scientific article.
(g) Would your conclusion have been different if you had chosen α = 0.01 instead of α = 0.05?