atistical Analysis II – Set # 2
Question 1 of 40Nonparametric statistical measures:
/ A. compare population means or proportions to determine the relationship between variables.
/ B. can only be used with independent samples.
/ C. allow for testing procedures that eliminate some of the unrealistic assumptions required for testing by parametric measures.
/ D. ignore individual measures, and, instead, focus on computed summary statistics of the populations being measured.
Question 2 of 40
The chi-square distribution:
/ A. compares sample observations to the expected values of a given variable.
/ B. can be used to analyze both ordinal and nominal level data.
/ C. is normally distributed.
/ D. Both A and B
Question 3 of 40
The chi-square test statistic:
/ A. is computed from the actual and expected frequencies of the given set of data.
/ B. is computed from the same distribution regardless of the number of degrees of freedom involved.
/ C. is more commonly used for quantitative population variables.
/ D. does not measure independence between events normal distribution (Wilcoxon matched-pair signed rank test).
Question 4 of 40
Use the following data to answer questions 4-6:
A random sample of cars passing through a service station showed the following results:
Blue / Red / Gray / Black / White / Green
18 / 24 / 16 / 21 / 23 / 18
For a X2 goodness-of-fit test, the null hypothesis is:
/ A. there are more red cars on the road than any other color of car.
/ B. the distribution of colors for cars on the road is uneven.
/ C. there is an even number of cars on the road for all given colors.
/ D. None of the above
Question 5 of 40
The expected frequency for each color of car is:
/ A. 10.
/ B. 12.
/ C. 20.
/ D. 24.
Question 6 of 40
The computed value of X2 is ______indicating that we should ______the null hypothesis.
/ A. 0; reject
/ B. 2.5; fail to reject
/ C. 5.41; fail to reject
/ D. 12.5; fail to reject
Question 7 of 40
The X2 distribution:
/ A. is normally distributed for observation sets with unequal expected frequencies.
/ B. is normally distributed for large sample sizes.
/ C. is negatively skewed for small sample sizes and a low number of degrees of freedom.
/ D. approaches a normal distribution as the number of degrees of freedom increases.
Question 8 of 40
The X2 distribution:
/ A. can be applied to observation sets where the expected frequencies of only 3 of 10 observations is less than 5.
/ B. should not be used in experiments with two cells with expected frequencies of less than 5.
/ C. can be used as long as (fo- fe)2 is large.
/ D. cannot be used if the expected frequencies are unequal.
Question 9 of 40
A contingency table:
/ A. is constructed from the expected frequencies of a variable.
/ B. uses actual total population data to develop a hypothesis for dependence or independence.
/ C. allows for statistical determinations to be made without the use of a test statistic.
/ D. shows the frequency level of every possible combination of attributes in a given set of data.
Question 10 of 40
A question has these possible choices — excellent, very good, good, fair, and unsatisfactory. How many degrees of freedom are there using the goodness-of-fit test to the sample results?
/ A. 0
/ B. 2
/ C. 4
/ D. 5
Question 11 of 40
What is the critical value at the 0.05 level of significance for a goodness-of-fit test if there are six categories?
/ A. 3.841
/ B. 5.991
/ C. 7.815
/ D. 11.070
Question 12 of 40
A distributor of personal computers has five locations in the city. The sales in units for the first quarter of the year were as follows:
Location / Observed Sales (Units)
North Side / 70
Pleasant Township / 75
Southwyck / 70
I-90 / 50
Venice Avenue / 35
Total / 300
What is the critical value at the 0.01 level of risk?
/ A. 7.779
/ B. 15.033
/ C. 13.277
/ D. 5.412
Question 13 of 40
What is our decision for a goodness-of-fit test with a computed value of chi-square of 1.273 and a critical value of 13.388?
/ A. Do not reject the null hypothesis
/ B. Reject the null hypothesis
/ C. Unable to reject or not reject the null hypothesis based on data
/ D. Should take a larger sample
Question 14 of 40
A student asked the statistics professor if grades were marked “on the curve.” The professor decided to give the student a project to determine if last year's statistics grades were normally distributed. The professor told the student to assume a mean of 75 and a standard deviation of 10 and to use the following results.
Letter Grade / Grade Average / Observed / Expected
Over 100 / 0 / 0.70
A / 90 up to 100 / 15
B / 80 up to 90 / 20
C / 70 up to 80 / 40
D / 60 up to 70 / 30
F / 50 up to 60 / 10 / 7.00
Under 50 / 0 / 0.00
What is the null hypothesis?
/ A. Observed grades are not normally distributed.
/ B. Observed grades are normally distributed with a mean = 75 and a standard deviation = 10.
/ C. Observed grades are normally distributed with a mean = 80 and a standard deviation = 10.
/ D. Observed grades are normally distributed with a mean = 70 and a standard deviation = 10.
Question 15 of 40
Using the results in Question #14, what is the expected number of B's?
/ A. 44.0
/ B. 14.5
/ C. 12.6
/ D. 27.8
Question 16 of 40
Use the following to answer Questions 16–20:
Recently, students in a marketing research class were interested in the driving behavior of students driving to school. Specifically, the marketing students were interested if exceeding the speed limit was related to gender. They collected the following responses from 100 randomly selected students:
Speeds / Does Not Speed
Males / 40 / 25
Females / 10 / 25
What is the null hypothesis for the analysis?
/ A. There is no relationship between gender and speeding.
/ B. The correlation between gender and speeding is zero.
/ C. As gender increases, speeding increases.
/ D. The mean of gender equals the mean of speeding.
Question 17 of 40
The degrees of freedom for the analysis is/are:
/ A. 1.
/ B. 2.
/ C. 3.
/ D. 4.
Question 18 of 40
Using 0.05 as the significance level, what is the critical value for the test statistic?
/ A. 3.841
/ B. 5.991
/ C. 7.815
/ D. 9.488
Question 19 of 40
What is the value of the test statistic?
/ A. 100
/ B. 9.89
/ C. 50
/ D. 4.94
Question 20 of 40
Based on the analysis, what can be concluded?
/ A. Gender and speeding are correlated.
/ B. Gender and speeding are not related.
/ C. Gender and speeding are related.
/ D. No conclusion is possible.
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Question 21 of 40The ______test is useful for before/after experiments.
/ A. goodness-of-fit
/ B. sign
/ C. median
/ D. chi-square
Question 22 of 40
The ______test is useful for drawing conclusions about data using nominal level of measurement.
/ A. goodness-of-fit
/ B. sign
/ C. median
/ D. chi-square
Question 23 of 40
In an experiment, a sample size of 10 is drawn, and a hypothesis test is set up to determine: H0 : p = 0.50; H1:p < or = 0.50; for a significance level of.10, the decision rule is as follows:
/ A. Reject H0 if the number of successes is 2 or less.
/ B. Reject H0 if the number of successes is 8 or more.
/ C. Reject H0 if the number of successes is three or less.
/ D. Reject H0 if the number of successes is less than 2 or more than 8.
Question 24 of 40
For a "before and after" test, 16 of a sample of 25 people improved their scores on a test after receiving computer-based instruction. For H0 : p = 0.50; H1:pis not equal to 0.50; and a significance level of .05:
/ A. z = 1.2, fail to reject the null hypothesis.
/ B. z = 1.4, reject the null hypothesis.
/ C. z = 1.4, fail to reject the null hypothesis.
/ D. z = 1.64, reject the null hypothesis.
Question 25 of 40
A sample group was surveyed to determine which of two brands of soap was preferred. H0 :p = 0.50; H1: p is not equal to 0.50. Thirty-eight of 60 people indicated a preference. At the .05 level of significance, we can conclude that:
/ A. z = 0.75, fail to reject H0.
/ B. z = 1.94, fail to reject H0.
/ C. z = 1.94, reject H0.
/ D. z = 2.19, reject H0.
Question 26 of 40
The performance of students on a test resulted in a mean score of 25. A new test is instituted and the instructor believes the mean score is now lower. A random sample of 64 students resulted in 40 scores below 25. At a significance level of α = .05:
/ A. H0 : p = 0.50; H1:p < 0.50.
/ B. H0 : p = 0.50; H1:p > 0.50.
/ C. H0 : p = 25; H1:p > 25.
/ D. H0 : p = 25; H1:p < 25.
Question 27 of 40
From the information presented in question #6:
/ A. z = 3.75, we can reject the null hypothesis.
/ B. z = 1.875, we fail to reject the null hypothesis.
/ C. z = -1.625, we fail to reject the null hypothesis.
/ D. z = -1.875, we can reject the null hypothesis.
Question 28 of 40
A golf club manufacturer claims that the median length of a drive using its driver is 250 yards. A consumer group disputes the claim, indicating that the median will be considerably less. A sample of 500 drives is measured; of these 220 were above 250 yards, and none was exactly 250 yards. The null and alternate hypotheses are:
/ A. Ho: 0 = 250; H1: 0 < 250.
/ B. Ho: median = 250; H1: median > 250.
/ C. Ho: 0 > 250; H1: 0 < 250.
/ D. Ho: median = 250; H1: median < 250.
Question 29 of 40
From the information presented in question #8, using a level of significance = .05:
/ A. z = -1.74; we should fail to reject the null hypothesis.
/ B. z = 2.64; we should fail to reject the null hypothesis.
/ C. z = -2.72; we should fail to reject the null hypothesis.
/ D. z = -3.17; we should reject the null hypothesis.
Question 30 of 40
The Wilcoxon rank-sum test:
/ A. is a nonparametric test for which the assumption of normality is not required.
/ B. is used to determine if two independent samples came from equal populations.
/ C. requires that the two populations under consideration have equal variances.
/ D. Both A and B
Question 31 of 40
A nonparametric test which can evaluate ordinal-scale data of a non-normal population is called the:
/ A. Wilcoxon signed rank test.
/ B. Kruskal-Wallis test.
/ C. sign test.
/ D. median test.
Question 32 of 40
A researcher wishes to test the differences between pairs of observations with a non-normal distribution. She should apply the:
/ A. Wilcoxon signed rank test.
/ B. Kruskal-Wallis test.
/ C. Wilcoxon rank-sum test.
/ D. t test.
Question 33 of 40
The data below indicate the rankings of a set of employees according to class theory and on-the-job practice evaluations:
Theory / 1 / 7 / 2 / 10 / 4 / 8 / 5 / 3 / 6 / 9
Practice / 2 / 8 / 1 / 7 / 3 / 9 / 6 / 5 / 4 / 10
What is the Spearman correlation of coefficient for the data?
/ A. -0.0606
/ B. 0.1454
/ C. 0.606
/ D. 0.8545
Question 34 of 40
For the value of rs determined, a test of significance indicates that:
/ A. t = -0.45, a weak negative relationship between the two variables.
/ B. t = - 0.06, a strong negative relationship between the variables.
/ C. t = 0.45, a weak positive relationship between the two variables.
/ D. t = 4.65, a strong positive relationship between the variables.
Question 35 of 40
To determine whether four populations are equal, a sample from each population was selected at random and using the Kruskal-Wallis test, H was computed to be 2.09. What is our decision at the 0.05 level of risk?
/ A. Fail to reject the null hypothesis because 0.05 < 2.09
/ B. Fail to reject the null hypothesis because 2.09 < 7.815
/ C. Reject the null hypothesis because 7.815 is > 2.09
/ D. Reject the null hypothesis because 2.09 > critical value of 1.96
Question 36 of 40
A soap manufacturer is experimenting with several formulas of soap powder and three of the formulas were selected for further testing by a panel of homemakers. The ratings for the three formulas are as follows:
A / 35 / 36 / 44 / 42 / 37 / 40
B / 43 / 44 / 42 / 32 / 39 / 41
C / 46 / 47 / 40 / 36 / 45 / 49
What is the value of chi-square at the 5% level of significance?
/ A. 6.009
/ B. 6
/ C. 5.991
/ D. 5
Question 37 of 40
Which of the following values of Spearman's coefficient of rank correlation indicates the strongest relationship between two variables?
/ A. –0.91
/ B. –0.05
/ C. +0.64
/ D. +0.89
Question 38 of 40
Suppose ranks are assigned to a set of data from low to high with $10 being ranked 1, $12 being ranked 2, and $21 being ranked 3. What ranks would be assigned to $26, $26 and $26?
/ A. 4, 5, 6
/ B. 4, 4, 4
/ C. 5, 5, 5
/ D. 5.5, 5.5, 5.5
Question 39 of 40
Two movie reviewers gave their ratings (0 to 4 stars) to ten movies released this past month as follows:
Movie / A / B / C / D / E / F / G / H / I / J
S's Rating / 4 / 2 / 3.5 / 1 / 0 / 3 / 2.5 / 4 / 2 / 0
T's Rating / 3 / 3 / 3 / 2.5 / 1.5 / 3.5 / 4 / 3 / 2 / 1
What is the rank order correlation?
/ A. 48
/ B. 0.7091
/ C. 2.306
/ D. 2.844
Question 40 of 40
What is a requirement that must be met before the Kruskal-Wallis one-way analysis of variance by ranks test can be applied?
/ A. Populations must be normal or near normal
/ B. Samples must be independent
/ C. Population standard deviations must be equal
/ D. Data must be at least interval level
21,22,26,27,29,31,32,34,35,36,40
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