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MCQs: Chi-square Distribution

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1. Nonparametric statistical measures: (Points: 5)
compare population means or proportions to determine the relationship between variables.
can only be used with independent samples.
allow for testing procedures that eliminate some of the unrealistic assumptions required for testing by parametric measures.
ignore individual measures, and, instead, focus on computed summary statistics of the populations being measured.

2. The chi-square distribution: (Points: 5)
compares sample observations to the expected values of a given variable.
can be used to analyze both ordinal and nominal level data.
is normally distributed.
Both A and B

3. The chi-square test statistic: (Points: 5)
is computed from the actual and expected frequencies of the given set of data.
is computed from the same distribution regardless of the number of degrees of freedom involved.
is more commonly used for quantitative population variables.
does not measure independence between events normal distribution (Wilcoxon matched-pair signed rank test).

4. 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: (Points: 5)
there are more red cars on the road than any other color of car.
the distribution of colors for cars on the road is uneven.
there is an even number of cars on the road for all given colors.
None of the above

5. The expected frequency for each color of car is: (Points: 5)

6. The computed value of X2 is __________ indicating that we should __________ the null hypothesis. (Points: 5)
0; reject
2.5; fail to reject
5.41; fail to reject
12.5; fail to reject

7. The X2 distribution: (Points: 5)
is normally distributed for observation sets with unequal expected frequencies.
is normally distributed for large sample sizes.
is negatively skewed for small sample sizes and a low number of degrees of freedom.
approaches a normal distribution as the number of degrees of freedom increases.

8. The X2 distribution: (Points: 5)
can be applied to observation sets where the expected frequencies of only 3 of 10 observations is less than 5.
should not be used in experiments with two cells with expected frequencies of less than 5.
can be used as long as (fo- fe)2 is large.
cannot be used if the expected frequencies are unequal.

9. A contingency table: (Points: 5)
is constructed from the expected frequencies of a variable.
uses actual total population data to develop a hypothesis for dependence or independence.
allows for statistical determinations to be made without the use of a test statistic.
shows the frequency level of every possible combination of attributes in a given set of data.

10. A question has these possible choices â?" excellent, very good, good, fair, and unsatisfactory. How many degrees of freedom are there using the goodness-of-fit test to the sample results? (Points: 5)

11. What is the critical value at the 0.05 level of significance for a goodness-of-fit test if there are six categories? (Points: 5)

12. 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? (Points: 5)

13. 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? (Points: 5)
Do not reject the null hypothesis
Reject the null hypothesis
Unable to reject or not reject the null hypothesis based on data
Should take a larger sample

14. A student asked the statistics professor if grades were marked â??on the curve.â? 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? (Points: 5)
Observed grades are not normally distributed.
Observed grades are normally distributed with a mean = 75 and a standard deviation = 10.
Observed grades are normally distributed with a mean = 80 and a standard deviation = 10.
Observed grades are normally distributed with a mean = 70 and a standard deviation = 10.

15. Using the results in Question #14, what is the expected number of B's? (Points: 5)

16. Use the following to answer Questions 16â?"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?

(Points: 5)
There is no relationship between gender and speeding.
The correlation between gender and speeding is zero.
As gender increases, speeding increases.
The mean of gender equals the mean of speeding.

17. The degrees of freedom for the analysis is/are: (Points: 5)

18. Using 0.05 as the significance level, what is the critical value for the test statistic? (Points: 5)

19. What is the value of the test statistic? (Points: 5)

20. Based on the analysis, what can be concluded? (Points: 5)
Gender and speeding are correlated.
Gender and speeding are not related.
Gender and speeding are related.
No conclusion is possible.

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The solution provides answers to multiple choice questions on chi-square distribution. Relevant workings are also included.

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