Exam Prep Ch.17 Kumar Hypothesis Testing Basics

Test Bank

CHAPTER 17 - Hypothesis Testing: Basic Concepts and Tests of Association

True-False

1. Assuming the hypothesis to be true, the significance level indicates the percentage

of sample means that are outside the cutoff limits.

2. The hypothesis test serves to quantify the reliability of research

results, indicating the extent to which the data support the

empirical findings.

3. The process of hypothesis testing, begins with an assumption about

sample statistic

4. A high p-value means that the probability of a statistically

significant difference is high.

5. The purpose of hypothesis testing is not to question the computed value

of the sample statistic but to make a judgment about the difference between that

sample statistic and the hypothesized population parameter.

6. In order to reduce the probability of committing a Type II error, the probability of

committing a Type I error must necessarily decreased

7. The Chi square test can provide a useful measurement of association.

8. The number of degrees of freedom, v, for the chi‐square test of independence

is obtained using the formula v = (r -1) * (c -1).

9. A major advantage of the Chi square statistic as a measurement of

association between two questions is that it is independent of the

sample size, making it easy to interpret in an absolute sense.

10. Two branches of a major multinational corporation conducted surveys

to measure the association between income level (low, mid, high) and

need for a certain produce (low, mid, high). The sample size in one

survey was 100 and in the other, 200. The branches now wish to

compare the two cross tabulations that were generated from the

surveys. Given this information, the Chi square statistic would

provide an easy-to-interpret method to compare the associations.

11. The null hypothesis associated with the sample Chi square statistic

is that the two (intervally scaled) variables are statistically

independent.

12. If the p-value is less than or equal to 0.05, then it is valid to

say that the sample evidence is significant at .05 level.

13. The contingency coefficient varies between 0 and 1. The 0 value occurs in the case

of no association (i.e., the variables are statistically independent), but the maximum

value of 1 is never achieved.

14. A p-value of .005 proves that the null hypothesis is false.

15. A p-value of .45 means that the evidence against the null hypothesis

is very weak.

16. The higher the significance level used for testing a hypothesis, the

higher is the probability of rejecting the null hypothesis when it

is true.

17. Type II error occurs when the null hypothesis is not rejected when

it is false.

18. A high value of b indicates that the test of hypothesis is working

very well.

19. Degrees of freedom refers to the number or bits of "free" or

unconstrained data used in calculating a sample statistic.

20. The larger the degrees of freedom, the lower is the likelihood of

observing differences among the variables.

21. The Chi square test cannot be used to ascertain whether the observed

pattern fits with the expected pattern.

22. Hypothesis testing can be used to establish whether the null

hypothesis is true or false.

Multiple Choice

1. Given the following 2 X 2 contingency table

Q1

yes no

yes 23 36 59

Q2 no 46 15 61

69 51

What would be the expected number of people that said yes to both the questions

if your null hypothesis stated that you expected an equal number in all cells ?

1. 25
2. 30
3. 33.9
4. 40
5. not enough information given to test this hypothesis
6. For data in the previous question, what would the overall chi-square value

be for the whole table if the expected value for the Q1 yes - Q2 yes cell was equal to 23 ?

1. 0.0
2. 1.0
3. 5.0
4. 9.9
5. some number greater than 10.0
6. An index that is calculated from sample data and whose value determines whether to

accept or reject a null hypothesis is

1. test statistic
2. critical value
3. significance level
4. decision rule
5. If the researcher, in making a statistical test, rejects a true hypothesis, the error

is called

1. Type I error
2. Type II error
3. Type III error
4. no error is made
5. none of the above

Use the following information to answer questions 5 - 9

Assume you are doing a chi-square test for independence between class and grade. Given

the following data collected by sample survey methods, answer the following questions.

Class

I II

A 14 6

B 25 15

Grade C 60 20

D 34 6

E 17 3

1. What is the probability of making a C and being in class II ?
2. .05
3. .10
4. .25
5. .40
6. .50
7. What is the expected value of the cell representing a grade of B for class II ?
8. 5
9. 10
10. 20
11. 40
12. 50
13. If the expected value for a grade of A for a class II was 3, the cell’s

chi-square would be

1. ½
2. 1
3. 2
4. 3
5. 9

8. The degrees of freedom for this table is

1. 1
2. 2
3. 4
4. 5
5. 10
6. If the computed χ2 value for this table was 8.7 and the value from the back of the

book with the correct degrees of freedom was 9.49 with α = 0.05 you would

1. accept the null hypothesis that grade and class are correlated
2. reject the null hypothesis that grade and class are correlated
3. accept the null hypothesis that grade and class are independent
4. reject the null hypothesis that grade and class are independent
5. it is too close to tell whether to accept or reject

10. New Products Incorporated ran a test market for their latest product

in two markets, City A and City B. Both have equal populations. The

average weekly sales were $1,000 and $800, respectively, in the two

cities. Based on this information, we can say that

1. sales in City A are significantly higher than sales in City B.

2. the difference in the sales level could be due to

sampling error.

3. the difference in the sales level may be due to the fact

that the residents of City B accepted the product to

lesser degree than those of City A.

a. 1

b. 2

c. 3

d. 1and 3

e. 2 and 3

11. The basic steps recommended in hypothesis testing, in the correct

order, are

a. analyze data which support an alternative hypothesis or position, conceptualize a null hypothesis, raise the question of the probability that the empirical "evidence" supporting the original position could have been a statistical accident, calculate the p-value.

b. estimate a p-value, develop and analyze data, conceptualize a null hypothesis, cluster the data into two testable groups.

c. conceptualize a null hypothesis, raise the question of the probability that the empirical "evidence" supporting the original position could have been a statistical accident, develop and analyze data, calculate the p-value.

d. cluster the data into two or three groups, analyze the data, calculate the p-value, test the null hypothesis.

e. cluster the data into as many groups as needed, develop and analyze the data, raise the question of the probability that the empirical "evidence" supporting the original position could have been a statistical accident, calculate the p-value.

12. The criterion (criteria) to use while making the decision to reject or not to reject the a null hypothesis is (are)

1. significance level

2. number of degrees of freedom

3. one or two tailed test

1. 1
2. 2
3. 3
4. 1 and 2
5. all of the above

Use the following information for questions 13 through 16

13. 1. The marginal distribution for F is .2 (often), .5 (occasional), .3 (seldom).

2. The marginal distribution for F is .5 (often), .5 (occasional), 0.0 (seldom).

3. The marginal distribution for L is .5 (convenient), .5 (not convenient).

4. The marginal distribution for L is .2 (convenient), .8 (not convenient).

a. 1

b. 2

c. 3

d. 4

e. 1 and 3

14. According to the data above, which of the following is true?

1. E (convenient, often) = E (often, convenient)

2. E (seldom, not convenient) = 30

3. E (seldom, not convenient) = 20

4. E (convenient, occasional) = 50

a. 1

b. 2

c. 3

d. 4

e. 1 and 2

15. According to the data above, which of the following is true?

Let χ² = Σ (O_i - E_i)²

E_i

a. The χ² statistic can be used to test the hypothesis that F and L

are independent.

b. The χ2 statistic can be used to test the hypothesis that

frequent shopper is more likely to go shopping if the location is convenient.

c. The t-statistic can be used most appropriately to test the

hypothesis that F and L are independent.

d. The t-statistic can be used to test the hypothesis that shopping

is independent of convenience.

e. None of the above

16. For the data above, which of the following statements is true?

1. The χ² statistic is 4.167.

2. The χ² statistic is 6.25.

3. The p-value is less than 0.01.

a. 1

b. 2

c. 3

d. 1 and 3

e. 2 and 3

17. The manager of the marketing division of Acme Corporation forecasts

an average monthly sales in 1978 of $65,000. In the first seven

months of 1978, the average monthly sales were $63,200, with

standard deviation of $500. The management wishes to test the

hypothesis H_o that "statistically" the manager was right (H_o:

μ = 65,000) against the alternative hypothesis that he was wrong in

his forecast (H_o: μ = 65,000), using a two-tail test. Assuming

normal distribution of monthly sales, which of the following statements is true?

a. H_o is rejected at the 5 percent significance level but accepted

at the 1 percent significance level.

b. H_o is accepted at both the 5 percent and 1 percent significance levels.

c. H_o is accepted at the 5 percent significance level but rejected

at the 1 percent significance level.

d. H_o is rejected at both the 5 percent and 1 percent significance levels.

e. None of the above.

18. The Berkeley Supermarket buys its supplies of potatoes from two

different farms, A and B. In a recent sampling test, it was found that the sample taken from Farm A had a mean weight of 10 ounces per potato, whereas the sample from Farm B had a mean weight of 10.3 ounces. In view of this test, is there a statistically discernible difference (at the 95 percent confidence level) between the mean weights of the potatoes of the two farms?

a. Yes.

b. No, because the difference of 0.3 ounces is very small compared

to the mean (approximately 3 percent).

c. The standard deviations of both samples must be known (the sample

sizes are irrelevant) before the above question can be answered.

d. Both the standard deviations and sample sizes must be known

before the above question can be answered.

e. Even if both the standard deviations and sample sizes were known,

the above question cannot be answered.

Use the following information for questions 19 through 21.

A subscription service stated that preferences for different national magazines were independent of geographical location. A survey was taken in which 300 respondents randomly chosen from three areas were given a choice among three different magazines. Each person expressed his or her favorite. The following results were obtained:

19. If the appropriate null hypothesis for a chi-square test were not

rejected, the following would be implied:

1. Subscription for magazine X = subscription for magazine

Y = subscription for magazine Z.

2. The probability of magazine preference (unconditional on location) is equal to the probability of magazine preference (conditional on location).

3. Magazine preferences are uncorrelated with location.

a. 1

b. 2

c. 3

d. 2 and 3

e. 1, 2, and 3

20. The number of degrees of freedom is

a. 4

b. 6

c. 7

d. 9

e. none of the above

21. Suppose the chi-square value for the above test is 15; this will

yield a significance level closest to the value

a. .1

b. .05

c. .01

d. .005

e. .001

22. To overcome the problem of the chi-square value being directly proportional to the sample size, the following measure(s) has (have) been developed:

a. Phi-squared

b. Contingency coefficient

c. Cramer’s V

d. Only 1 and 2

e. all of the above

23. Accepting a null hypothesis when it is false is called a(n)

a. type I error.

b. type II error.

c. hypothesis error.

d. power of the test.

e. significance level.

24. The limitation of chi square as an association measure is

1. it is hard to compare cross-tabulations with different sample sizes.

2. it doesn't indicate how the variables are related.

3. it is difficult to obtain a feel for its value (since it has no upper bound).

a. 1

b. 2

c. 3

d. 1, 2, and 3

e. 1 and 2 only