Deck 17: Hypothesis Testing: Basic Concepts and Tests of Association

Question 1

The null hypothesis associated with the sample Chi square statistic is that the two intervally scaled.variables are statistically independent.

Answer 1

False

Question 2

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.

Answer 2

False

Question 3

Degrees of freedom refers to the number or bits of "free" or unconstrained data used in calculating a sample statistic.

Answer 3

True

Question 4

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.

Question 5

The higher the significance level used for testing a hypothesis, the higher is the probability of rejecting the null hypothesis when it is true.

Question 6

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

Question 7

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

Question 8

A high p-value means that the probability of a statistically significant difference is high.

Question 9

The larger the degrees of freedom, the lower is the likelihood of observing differences among the variables.

Question 10

A p-value of .45 means that the evidence against the null hypothesis is very weak.

Question 11

The hypothesis test serves to quantify the reliability of research results, indicating the extent to which the data support the empirical findings.

Question 12

If an analyst computes "marginal," he or she simply computes frequency distributions for the individual questions.

Question 13

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.

Question 14

The confidence with which we may reject/accept a hypothesis is independent of the sample size, but dependent on the true population variance.

Question 15

If the sample size increases, the p-value will usually become smaller.

Question 16

After analyzing repeat purchase sales data from two market segments, the researcher reported that the p-value was 0.15.This implies that there are more than 15 chances out of 100 that the difference found was simply due to a sampling accident.

Question 17

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

Question 18

A p-value of .07 means that the results are statistically significant at the 0.05 level. Assume that a new product is placed in a sample of stores.The sample mean for units sold is 35 units.We test the hypothesis that the population mean is only 20.

Question 19

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

Question 20

We can be more confident in rejecting the null hypothesis with a p-value of 0.05 than with a p-value of 0.02.

Question 21

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 a standard deviation of $500.The management wishes to test the hypothesis H_o that "statistically" the manager was right H_o: $\mu$ = 65,000) against the alternative hypothesis that he was wrong in his forecast H_o: $\mu$ = 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.

Question 22

Hypothesis testing can be used to establish whether the null hypothesis is true or false.

Question 23

Use the following information for questions


-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

Question 24

An index that is calculated from sample data and whose value determines whether to accept or reject a null hypothesis is a

A)test statistic
B)critical value
C)significance level
D)decision rule

Question 25

Use the following information for questions
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:


-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

Question 26

Use the following information for questions
Observation

The numbers in each cell represent the sales level in thousands of
dollars.

-Which of the following is/are true? 1-The sum of squares within rows will be given by 5 3 _ $\Sigma$$\Sigma$ X_ip - X_p)² i=1 p=1 2-The sum of squares within rows will be given by 3 _ $\Sigma$ X_p - X)² p=1 3-The sum of squares within rows will be given by 5 5 _ $\Sigma$$\Sigma$ X_ip - X)² i=1 p=1 4- 5 3 _ 5 3 _ 3 _ _ $\Sigma$ $\Sigma$ X_ip - X)² = $\Sigma$ $\Sigma$ X_ip - X_p)² + $\Sigma$ X_p - X)² i=1 p=1 i=1 p=1 p=1

A)1
B)2
C)3
D)4
E)1 and 4

Question 27

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 ?

A)0.0
B)1.0
C)5.0
D)9.9
E)some number greater than 10.0

Question 28

Use the following information for questions
Observation

The numbers in each cell represent the sales level in thousands of
dollars.

-Which of the following is/are true? 1-The appropriate null hypothesis would state, "Advertising levels have no effect on sales." 2-The appropriate null hypothesis would state, "There is an increase in the sales level due to an increase in the intensity of the advertising effort." 3-The appropriate statistic to test the null hypothesis would be $\chi$ ² with 8 degrees of freedom.

A)1
B)2
C)3
D)1 and 3
E)2 and 3

Question 29

If the researcher, in making a statistical test, rejects a true hypothesis, the error is called

A)Type I error
B)Type II error
C)Type III error
D)no error is made
E)none of the above

Question 30

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.

Question 31

Use the following information for questions


-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

Question 32

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 a 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 a lesser degree than those of City A.

A)1
B)2
C)3
D)1and 3
E)2 and 3

Question 33

Use the following information for questions
Observation

The numbers in each cell represent the sales level in thousands of
dollars.

-Which of the following statements is/are true? 1-MSS within rows) = MSS μ = 500 MSS between rows) = MSS_r = 12.67 Total sum of squares = 1,152 2-MSS_r = 500, MSS _$\mu$ = 12.67, F = 37.5 3-The appropriate test statistic is F with 2 and 8 degrees of freedom 4-The appropriate test statistic is F with 2 and 12 degrees of freedom

A)1
B)2
C)3
D)4
E)2 and 4

Question 34

Use the following information for questions


-For the data above, which of the following statements is true? 1-The $\chi$ ² statistic is 4.167. 2-The $\chi$ ² 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

Question 35

a If $\mu$ _x = 10, n = 16 σ _x² = 10, n = 16 The p-value for a sample observation of X = 11, based on the null hypothesis that the sample was drawn from the above population, would be closest to

A).3
B).45
C).005
D).05
E).68

Question 36

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 ?

A)25
B)30
C)33.9
D)40
E)not enough information given to test this hypothesis

Question 37

The Chi square test cannot be used to ascertain whether the observed pattern fits with the expected pattern.

Question 38

The p-value is closest to

A).99
B).95
C).05
D).01
E).001

Question 39

Use the following information for questions


-According to the data above, which of the following is true? Let $\chi$ ² = $\Sigma$ O_i - E_i)² E_i

A)The $\chi$ ² statistic can be used to test the hypothesis that F and L are independent.
B)The $\chi$ ² statistic can be used to test the hypothesis that a 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

Question 40

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.

Question 41

Use the following information for questions
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:


-The number of degrees of freedom is

A)4
B)6
C)7
D)9
E)none of the above

Question 42

Accepting a null hypothesis when it is false is called an)

A)type I error.
B)type II error.
C)hypothesis error.
D)power of the test.
E)significance level.

Question 43

Use the following information for questions
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:


-If the null hypothesis were true, the best guess at the number of respondents who prefer magazine X in the Northeast is closest to

A)75
B)100
C)125
D)150
E)none of the above

Question 44

Use the following information for questions
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:


-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

Question 45

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