# The Various Areas of Hypothesis Testing

(Statistical Techniques in Business & Economics, 11th ed.) Lind et al.

Nonparametric 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.

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. Can be used for ranked data.

e. Both a and b.

f. All of the above

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).

Use the following data to answer the next three questions:

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 of 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

The expected frequency for each color of car is:

a. 10

b. 12

c. 20

d. 24

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

e. 32.5; reject

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.

e. None of the above

The ?2 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.

e. Both a and b

f. All of the above

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.

Answer the next two questions using the following information:

A researcher catalogs responses on usage of e-mail communications in households with personal computers across four regions as follows:

Region

Level of Usage A B C D

Infrequent 26 46 12 6

Regular 88 60 32

Frequent 34 20 48 24

The expected value of the sample results for regular users of e-mail in region C is:

a. 5.33

b. 32.42

c. 43.17

d. 102

We should ___________the null hypothesis for the data, that e-mail use is independent of regional locations, at an alpha level of 0.05.

a. fail to reject

b. reject

The _____________test is useful for before/after experiments.

a. goodness of fit

b. sign

c. median

d. Chi square

The ______________test is useful for drawing conclusions about data using nominal level of measurements.

a. goodness of fit

b. sign

c. median

d. Chi square

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 a = .10, the decision rule is:

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.

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: p is not equal to 0.50; and a significance level of a = .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.

A sample group was surveyed to determine which of two brands of soap was preferred, i.e. H0 : p = .50; H1 : p > 0.50. 38 of 60 people indicated a preference, At the .a = .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

e. There is not enough information to formulate a conclusion

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 a = .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.

From the information presented in the above question:

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

e. we can make no conclusion concerning the median test score.

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 derives is measured, of these 220 were above 250 yards, and none were exactly 250 yards. The null and alternate hypotheses are:

a. H0: 0 = 250; H1: 0 < 250

b. H0: median = 250; H1 : median > 250

c. H0: 0 > 250; H1: 0 < 250

d. H0: median = 250; H1 : median < 250

Using a = .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 = 1.74; we should reject the null hypothesis

e. z = -3.17; we should reject the null hypothesis

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. Is used for experiments in which an initial measurement is followed by an intervention, and then a final measurement.

e. Both a. and b

f. All of the above

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

e. None of the above

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

e. None of the above

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

The Spearman correlation of coefficient for the data is:

a. -0.0606

b. 0.1454

c. 0.606

d. 0.8545

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.

#### Solution Summary

Multiple choice questions on testing of hypothesis. The questions are related to Null Hypothesis, Alternative Hypothesis, Significance Level, Critical Value, P value, Chi Square test, Nonparametric test & Test for Independence.