# Distributions, frequencies, critical values, and hypothesis tests.

10. 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

E) None of the above

11. Two chi-square distributions were plotted on the same chart. One distribution was for 3 degrees of freedom and the other was for 12 degrees of freedom. Which distribution would tend to approach a normal distribution?

A) 3 degrees

B) 12 degrees

C) 15 degrees

D) All would

E) None of the above

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

Pleasantway 75

Southwyck 70

I-90 50

Venice Avenue 35

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

E) None of the above

The following table shows the adjustment to civilian life and place of residence.

Residence After Adjustment to Civilian Life

Release From Prison Outstanding Good Fair Unsatisfactory

Hometown 27 35 33 25

Not hometown 13 15 27 25

Total 40 50 60 50

What is the critical value for this contingency table at the 0.01 level of significance?

A) 9.488

B) 2.070

C) 11.345

D) 13.277

E) None of the above

15. The educational level and the social activity of a sample of executives follow.

Social Activity

Education Above Average Average Below Average

College 30 20 10

High School 20 40 90

Grade School 10 50 130

What does the expected frequency for the "above average" social activity and "high school" education equal?

A) 9.50 D) 28.50

B) 60.00 E) None of the above

C) 22.50

16. Which of the following are true statements about the chi-square distribution?

A) Distribution is negatively skewed

B) Chi-square is based on two sets of degrees of freedom, one for the numerator and one for the denominator

C) Its shape is based on the degrees of freedom

D) All of the above are true

E) None of the above are true

17. Three new colors have been proposed for the Jeep Grand Cherokee vehicle. They are silvered-blue, almond, and willow green. The null hypothesis would be

A) willow green preferred over the other colors.

B) no preference among the colors.

C) any one color preferred over the other colors.

D) impossible to determine.

E) none of the above.

18. For a chi-square test involving a contingency table, suppose the null hypothesis is rejected. We conclude that the two variables are

A) linear.

B) curvilinear.

C) not related.

D) related.

E) none of the above.

19. The test whether two variables or characteristics are related results in

A) a contingency table.

B) a chi-square table.

C) an ANOVA table.

D) a scatter diagram.

E) none of the above.

20. In the chi-square test, the null hypothesis (no difference between sets of observed and expected frequencies) is rejected when the

A) computed chi-square is less then the critical value.

B) difference between the observed and expected frequencies is significant.

C) difference between the observed and expected frequencies is small.

D) difference between the observed and expected frequencies occurs by chance.

E) none of the above.

https://brainmass.com/statistics/contingency-table/questions-on-statistics-distributions-frequencies-critical-values-and-hypothesis-tests-210206

#### Solution Preview

10. 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 [ Answer : D ]

B) 5.991

C) 7.815

D) 11.070

E) None of the above

Explanation:

The degrees of freedom = 6 - 1 = 5

The critical value of chi-square for 5 degrees of freedom

At 0.05 significance level is 11.070(from chi-square table)

11. Two chi-square distributions were plotted on the same chart. One distribution was for 3 degrees of freedom and the other was for 12 degrees of freedom. Which distribution would tend to approach a normal distribution? [ Answer : B ]

A) 3 degrees

B) 12 degrees

C) 15 degrees

D) All would

E) None of the above

Explanation:

For large degrees of freedom the chi-square distribution is

Close to the normal distribution. Therefore, out of 3 and

12 degrees of freedom, it is close to normal distribution

for 12 degrees of freedom.

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

Pleasantway 75

Southwyck 70

I-90 50

Venice Avenue 35

300

What is the critical value at the 0.01 level of risk?

A) 7.779 [ Answer : C ...

#### Solution Summary

Distributions, frequencies, critical values and hypothesis tests are analyzed.

Chi Square Hypothesis Test

1. The student population at the state college consists of 55% females and 45% males.

A. A researcher recorded the gender of each student entering the theater and found a total of 385 females and 215 males. Report the chi-square value; do you reject the null hypothesis?

B. The same researcher also recorded the gender of each student watching a men's basketball game in the college gym and found a total of 83 females and 97 males. Report the chi-square value; do you reject the null hypothesis?

2. A researcher obtains information about registered drivers from the department of motor vehicle department reports the percentage of registered drivers in each age category as follows: 16% are under age 20; 28% are 20 to 29 years old; and 56% are age 30 or older. The number of accidents reports for each age group is as follows:

Under Age 20 Age 20-29 Age 30 or Older

68 92 140

A. Calculate and report the chi-square test statistic.

B. Do you reject or fail to reject the null hypothesis?

3. A researcher studies aggression contents in the dreams of men and women. The observed frequencies are:

Low Medium High

Females 18 4 2

Males 4 17 15

A. Calculate and report the chi-square test statistic.

B. Do you reject or fail to reject the null hypothesis?

4. A researcher obtains a sample of 200 students IQ scores and classified them as follows:

High Medium Low

Volunteer 43 73 34

Not Volunteer 7 27 16

A. Calculate and report the chi-square test statistic.

B. Do you reject or fail to reject the null hypothesis?

5. The following hypothetical data represent a sample of 50 individuals diagnosed with sschizophrenia and a sample of 100 people with no psychoric diagnosis. Each individual is also classified according to season in which he or she was born.

Summer Fall Winter Spring

No Disorder 26 24 22 28

Schizophrenia 9 11 18 12

B. Do you reject or fail to reject the null hypothesis?