Hello Dr. Mash,Attached is my last WebAssign homework from the statistics course. Student # 175861
1.
Write the formula for finding the expected frequency for a chi-square goodness-of-fit test.
fe = f0p
fe = r2n
fe = k − 1
fe =
| χ2 |
| n |
fe = Np
2.
How are the degrees of freedom computed for each test listed below?
(a) a chi-square goodness-of-fit test
df = (k1 − 1)(k2 − 1)
df = (n1 − 1)(n2 − 1)
df = N − 1
df = k − 1
df = n − 1
(b) a chi-square test for independence
df = k − 1
df = n − 1
df = (n1 − 1)(n2 − 1)
df = (k1 − 1)(k2 − 1)
df = N − 1
3.
Based on the scale of measurement for the data, which of the following tests is parametric? Which is nonparametric?
Part (a)
A researcher measures the average age that schizophrenia is diagnosed in a sample of male and female patients.
This test is parametric. This test is nonparametric.
Part (b)
A researcher measures the proportion of schizophrenic patients born in each season.
This test is parametric. This test is nonparametric.
Part (c)
A researcher tests whether frequency of Internet use and social interaction are independent.
This test is parametric. This test is nonparametric.
Part (d)
A researcher measures the amount of time (in seconds) that a group of teenagers uses the Internet for school-related and non-school-related purposes.
This test is parametric. This test is nonparametric.
4.
For each of the following examples, state whether the chi-square goodness-of-fit test or the chi-square test for independence is appropriate, and state the degrees of freedom (df) for the test.
Part (a)
An instructor tests whether class attendance (low, high) and grade point average (low, average, high) are independent.
State whether the chi-square goodness-of-fit test or the chi-square test for independence is appropriate.
chi-square goodness-of-fit chi-square test for independence
State the degrees of freedom for the test.
df = 
Part (b)
A student tests whether the professor's speaking style (monotone, dynamic) and student interest (low, average, high) are independent.
State whether the chi-square goodness-of-fit test or the chi-square test for independence is appropriate.
chi-square goodness-of-fit chi-square test for independence
State the degrees of freedom for the test.
df =
Part (c)
A health psychologist records the number of below average, average, and overweight individuals in a sample of college students.
State whether the chi-square goodness-of-fit test or the chi-square test for independence is appropriate.
chi-square goodness-of-fit chi-square test for independence
State the degrees of freedom for the test.
df =
Part (d)
A personality psychologist compares the number of single mothers with Type A or Type B personality traits.
State whether the chi-square goodness-of-fit test or the chi-square test for independence is appropriate.
chi-square goodness-of-fit chi-square test for independence
State the degrees of freedom for the test.
df =
5.
Students are asked to rate their preference for one of four video games. The following table lists the observed preferences in a sample of 80 students. State whether to retain or reject the null hypothesis for a chi-square goodness-of-fit test given the following expected frequencies. (Assume alpha equal to 0.05.)
|
| Video Games | |||
| McStats | Tic-Tac | Silly | Super | |
| Frequency | 20 | 20 | 20 | 20 |
(a) expected frequencies: 25%, 25%, 25%, 25%, respectively
Retain the null hypothesis.
Reject the null hypothesis.
(b) expected frequencies: 70%, 10%, 10%, 10%, respectively
Retain the null hypothesis.
Reject the null hypothesis.
6.
A local brewery produces three premium lagers named Half Pint, XXX, and Dark Night. Of its premium lagers, they bottle 40% Half Pint, 40% XXX, and 20% Dark Night lagers. In a marketing test of a sample of consumers, 35 preferred the Half Pint lager, 37 preferred the XXX lager, and 8 preferred the Dark Night lager. Using a chi-square goodness-of-fit test, decide to retain or reject the null hypothesis that production of the premium lagers matches these consumer preferences using a 0.05 level of significance.
State the value of the test statistic. (Round your answer to two decimal places.)
=
State the decision to retain or reject the null hypothesis.
Retain the null hypothesis. Reject the null hypothesis.
7.
A psychologist studying addiction tests whether cravings for cocaine and relapse are independent. The following table lists the observed frequencies in the small sample of people who use drugs.
| Obs. Freq. | Relapse |
| |||||
| Yes | No | ||||||
| Cravings | Yes | 20 | 10 | 30 | |||
| No | 8 | 15 | 23 | ||||
|
| 28 | 25 | N = 53 | ||||
(a) Conduct a chi-square test for independence at a 0.05 level of significance. (Round your answer to two decimal places.)=
Decide whether to retain or reject the null hypothesis.
Retain the null hypothesis. Reject the null hypothesis.
(b) Compute effect size using ϕ and Cramer's V. Hint: Both should give the same estimate of effect size. (If necessary, round your intermediate steps to two or more decimal places. Round your answers to two decimal places.)
| ϕ | = |
|
| V | = |
|
8.
A professor tests whether the loudness of noise during an exam (low, medium, and high) is independent of exam grades (pass, fail). The following table shows the observed frequencies for this test.
|
| Noise Level |
| ||||||||
| Low | Medium | High | ||||||||
| Exam | Pass | 21 | 16 | 9 | 46 | |||||
| Fail | 9 | 5 | 10 | 24 | ||||||
|
| 30 | 21 | 19 | N = 70 | ||||||
(a) Conduct a chi-square test for independence at a 0.05 level of significance. (Round your answer to two decimal places.)=
Decide whether to retain or reject the null hypothesis.
Retain the null hypothesis. Reject the null hypothesis.
(b) Compute effect size using Cramer's V. (Round your answer to two decimal places.)
V =
9.
What is Cramer's V for each of the following values for the chi-square test for independence? (Round your answers to two decimal places.)
(a)
X2 = 3.43, n = 70, dfsmaller = 1
V =
(b)
X2 = 7.98, n = 110, dfsmaller = 2
V =
(c)
X2 = 11.91, n = 190, dfsmaller = 3
V =
10.
Altamura, Dell'Osso, Vismara, and Mundo (2008) measured the relationship between gender and duration of untreated illness (DUI) among a sample of those suffering from major depressive disorder (MDD). The following table lists the observed frequencies from this study.
|
| Duration of |
| ||||||
| DUI ≤ 12 | DUI > 12 | |||||||
| Gender | Men | 20 | 5 | 25 | ||||
| Women | 55 | 33 | 88 | |||||
|
| 75 | 38 | N = 113 | |||||
Compute a chi-square test for independence at a 0.05 level of significance. (Round your answer to two decimal places.)=
Decide whether to retain or reject the null hypothesis.
Retain the null hypothesis. Reject the null hypothesis.
11.
What tests are appropriate for analyzing ordinal scale data?
variance tests nonparametric tests parametric tests regression tests interval tests
12.
Which nonparametric tests can be computed using a normal approximation formula to compute the test statistic? (Select all that apply.)
Mann-Whitney U test sign test Wilcoxon signed-ranks T test Friedman test Kruskal-Wallis H test
13.
State the appropriate nonparametric alternative test for each of the following parametric tests.
Part (a)
one-independent sample t-test
Mann-Whitney U test Friedman test two-sample sign test or Wilcoxon signed-ranks T test one-sample sign test Kruskal-Wallis H test
Part (b)
two-independent sample t-test
Kruskal-Wallis H test one-sample sign test Friedman test Mann-Whitney U test two-sample sign test or Wilcoxon signed-ranks T test
Part (c)
related samples t-test
one-sample sign test Kruskal-Wallis H test Mann-Whitney U test Friedman test two-sample sign test or Wilcoxon signed-ranks T test
Part (d)
one-way between-subjects ANOVA
Kruskal-Wallis H test Mann-Whitney U test two-sample sign test or Wilcoxon signed-ranks T test one-sample sign test Friedman test
Part (e)
one-way within-subjects ANOVA
one-sample sign test two-sample sign test or Wilcoxon signed-ranks T test Mann-Whitney U test Friedman test Kruskal-Wallis H test
14.
State the appropriate nonparametric test for each of the following examples.
Part (a)
A researcher measures the time it takes to complete a surgical procedure in a sample of surgeons with low, medium, or high skill level.
related samples sign test or Wilcoxon signed-ranks T test one-sample sign test Mann-Whitney U test Kruskal-Wallis H test Friedman test
Part (b)
A clinical researcher records the number of calories a group of obese patients consumes each day for 5 days.
one-sample sign test related samples sign test or Wilcoxon signed-ranks T test Kruskal-Wallis H test Friedman test Mann-Whitney U test
Part (c)
A social psychologist measures the time it takes children to complete a creativity task first in the presence and then in the absence of a parent.
one-sample sign test Kruskal-Wallis H test Mann-Whitney U test Friedman test related samples sign test or Wilcoxon signed-ranks T test
Part (d)
A cognitive psychologist measures the time it takes a sample of students to complete a memory task. The students were divided into one of three groups: A no distraction group, a moderate level of distraction group, and a high level of distraction group.
one-sample sign test Mann-Whitney U test Kruskal-Wallis H test related samples sign test or Wilcoxon signed-ranks T test Friedman test
15.
A community psychologist selects a sample of 16 local police officers to test whether their physical endurance is better than the median score of 73. She measures their physical endurance on a 100-point physical endurance rating scale.
| Performance Scores | |||
| 52 | 76 | 91 | 95 |
| 78 | 89 | 80 | 81 |
| 87 | 59 | 68 | 92 |
| 79 | 83 | 75 | 74 |
Based on the data given above, compute the one-sample sign test at a 0.05 level of significance.
x =
State whether to retain or reject the null hypothesis.
Retain the null hypothesis. Reject the null hypothesis.
16.
Practitioners measured spiritual well-being (SWB) in a sample of 16 adults who were alcoholic before and following treatment for alcoholism.
| Change in SWB | |
| +15 | −3 |
| +13 | +7 |
| +5 | +12 |
| +20 | +10 |
| −4 | +9 |
| +11 | +14 |
| +8 | +6 |
| −2 | −1 |
Use the normal approximation for the Wilcoxon signed-ranks T test to analyze the data above. (Round your answer to two decimal places.)
z =
State whether to retain or reject the null hypothesis. (Assume alpha equal to 0.05.)
Retain the null hypothesis. Reject the null hypothesis.
17.
A professor has a teaching assistant record the amount of time (in minutes) that a sample of 16 students engaged in an active discussion. The assistant observed 8 students in a class who used a slide show presentation and 8 students in a class who did not use a slide show presentation.
| With Microsoft | Without |
| 11 | 13 |
| 4 | 14 |
| 6 | 21 |
| 10 | 7 |
| 19 | 5 |
| 8 | 18 |
| 12 | 15 |
| 9 | 23 |
Use the normal approximation for the Mann-Whitney U test to analyze the data above. (Round your answer to two decimal places.)
z =
State whether to retain or reject the null hypothesis. (Assume alpha equal to 0.05.)
Retain the null hypothesis. Reject the null hypothesis.
18.
A statistics instructor measured student attitudes toward a statistics course prior to lectures, at the midterm, and after the final exam. Attitudes were measured on a 16-point scale, with higher scores indicating more positive attitudes toward the statistics course.
| Student | Prior to | At the | After the |
| A | 6 | 5 | 11 |
| B | 4 | 10 | 15 |
| C | 8 | 7 | 14 |
| D | 12 | 13 | 15 |
| E | 5 | 7 | 11 |
Based on the results shown in the table, test whether or not attitudes differed using the Friedman test at a 0.05 level of significance. (Round your answer to two decimal places.)
=
State whether to retain or reject the null hypothesis.
Retain the null hypothesis. Reject the null hypothesis.
