Deck 8: Hypothesis Testing II the Two-Sample Case

Question 1

In the two sample case, the null hypothesis is always about the difference in the

A) populations
B) samples
C) standard errors
D) all of the above

Answer 1

populations

Question 2

Samples of Republicans and Democrats have been tested for their level of support for welfare reform and the null hypothesis has been rejected. What may we conclude?

A) the difference is significant, there are differences between the parties on this issue
B) the difference is significant, the parties are the same on this issue
C) the difference is not significant
D) a Type I error has occurred

Answer 2

the difference is significant, there are differences between the parties on this issue

Question 3

Rejection of the null hypothesis in the two-sample case implies that the

A) samples are different on the trait of interest
B) populations from which the samples are drawn are different on the trait of interest
C) samples are not different on the trait of interest
D) populations from which the samples are drawn are not different on the trait of interest

Answer 3

populations from which the samples are drawn are different on the trait of interest

Question 4

When testing for the significance of the difference between two sample means, which parameters must be estimated with sample values?

A) the population standard deviations
B) the population means
C) the standard deviation of the sampling distribution
D) the alpha value

Question 5

For testing the difference between two sample means, the level of measurement is assumed to be

A) nominal
B) ordinal
C) interval-ratio
D) any of the above

Question 6

Random samples of men and women have been given a scale that measures their support for gun control. Men average 10.2 with standard deviation of 5.3. Women also average 10.2 but their standard deviation is 1.8. How could these results be dealt with appropriately?

A) test the difference in the sample means for statistical significance
B) since the sample means are the same value, there is no need to conduct any tests; these results cannot be significant
C) a one-tailed test of significance is called for
D) a test of significance with a very high alpha level ( $\alpha$ > 0.10) is called for

Question 7

When testing for the significance of the difference between two sample means, the standard deviation of the sampling distribution is estimated using

A) population standard deviations
B) the standard error of the means
C) degrees of freedom
D) sample standard deviations corrected for bias

Question 8

When conducting hypothesis tests for two sample means, the test statistic is

A) alpha
B) the difference in sample means
C) the degrees of freedom
D) the difference in the population means

Question 9

When testing for the significance of the difference between two samples, which is the proper assumption for step 1?

A) random sampling
B) ordinal level of measurement
C) degrees of freedom are zero
D) samples are independent as well as random

Question 10

When testing for the significance of the difference between two sample means, which of the following is almost always unknown?

A) the population standard deviations
B) the sample standard deviations
C) degrees of freedom
D) the sample means

Question 11

A researcher conducted a survey to determine if older people have different feelings about abortion than younger people. He used an alpha level of 0.05 (Z critical = $\pm$ 1.96) to test for significance and found that his computed test statistic was 2.76. He may conclude that

A) the difference occurred by random chance
B) the difference did not occur by random chance
C) the samples are not independent
D) the alpha level was too low

Question 12

When conducting hypothesis tests for two sample means, the term $\mu$ 1 - $\mu$ 2 in the numerator of the formula reduces to zero because

A) the standard deviations are calculated first
B) the tests are conducted at very low alpha levels
C) the samples are independent as well as random
D) the null hypothesis is assumed to be true

Question 13

Samples of Republicans and Democrats have been tested for their level of support for a new immigration policy. The test statistic is 0.54 and the critical region begins at ± 1.96. What may we conclude?

A) the difference is significant, there are differences between the parties on this issue
B) the difference is significant, the parties are the same on this issue
C) the difference is not significant
D) the difference is not significant and a Type I error has occurred

Question 14

When testing for the significance of the difference between two sample means, we must first estimate ___________ before we can compute the test statistic.

A) the standard deviation of the sampling distribution
B) the standard deviations of the samples
C) the population means
D) the critical region

Question 15

When testing for the significance of the difference between two sample means, the null hypothesis can be stated as

A) =

B) $\mu$ > 0
C) $\mu$ 1 = $\mu$ 2
D) $\sigma$ 1 = $\sigma$ 2

Question 16

When random samples are drawn so that the selection of a case for one sample has no effect on the selection of cases for another sample, the samples are

A) dependent
B) independent
C) simple
D) systematic

Question 17

The central problem in the case of two-sample hypothesis test is to determine

A) if the samples are random
B) if sample statistics are the same as those of the sampling distribution
C) if the parameters are representative of the populations
D) if two populations differ significantly on the trait in question

Question 18

To satisfy the requirement of independent random sampling, the researcher

A) must use only non-probability sampling
B) may randomly select cases from one list of the population, then subdivide that sample according to the trait of interest
C) may randomly select an entire neighborhood, then select any member of each family in that neighborhood
D) must select only very small populations

Question 19

When testing for the significance of the difference between two samples, the null hypothesis states that the ____________ are the same

A) sample means
B) population means
C) sampling distributions
D) population standard deviations

Question 20

When testing for the significance of the difference between two sample means, the null hypothesis is that

A) the sample standard deviations are different
B) the sample means are different
C) the populations from which the sample were drawn are different
D) the populations from which the sample were drawn are the same

Question 21

For all tests of hypothesis, the probability of rejecting the null hypothesis is a function of

A) the size of the observed differences
B) the alpha level and the use of one- or two-tailed tests
C) sample size
D) all of the above

Question 22

From a university population, random samples of 145 men and 237 women have been asked if they have ever cheated in a college class. 8% of the men and 6% of the women said that they have. What is the appropriate test to assess the significance of this difference?

A) test for the significance of the difference between two sample proportions, large samples
B) test for the significance of the difference between two sample proportions, small samples
C) test for the significance of the difference between two sample proportions, matched samples
D) test for the significance of the difference between two sample means, large samples

Question 23

Samples from two high schools are being tested for the difference in their average levels of prejudice. One sample contains 39 respondents and the other sample contains 47 respondents. The appropriate sampling distribution is the

A) t distribution
B) Z distribution
C) F distribution
D) any of the above

Question 24

For tests of significance involving two sample proportions, the value of the population proportion is estimated from

A) the value of the sample means
B) the value of Z (obtained)
C) the sample proportions
D) the sample standard deviations

Question 25

According to the text, on the issue of abortion,

A) Democratic and Republican opinion has grown increasingly alike over the years
B) Democratic and Republican opinion has grown increasingly apart over the years
C) Democratic women have become increasingly like Republican women
D) Young Democrats and young Republicans have become increasingly alike

Question 26

When testing the significance of the difference between two sample proportions, the null hypothesis is

A) Ps1 = Ps2
B) Ps1 = Ps21
C) Pu = (1 - Pu)
D) Pu1 = Pu2

Question 27

In testing for the significance of the difference between two sample means when the sample size is small, we may assume equal population variances if

A) sample sizes are exactly the same
B) sample sizes are varied
C) sample sizes are approximately equal
D) none of the above, we cannot assume equal population variance

Question 28

According to the text, reading tests conducted on representative samples of American 4th graders show

A) no significant improvement between 2008 and 2012
B) a significant decrease in scores since 2008
C) a significant increase in scores since 2008
D) an increase in average scores for boy since 2008 but not for girls

Question 29

Since critical values of t vary by sample size, before using the t table we must first calculate

A) the Z score
B) degrees of freedom
C) the population standard deviation
D) the alpha level

Question 30

When is the t distribution used instead of the Z distribution to test the significance of the difference between two sample means?

A) never
B) when sample size is very large
C) when one sample is much larger than the other
D) when N is small

Question 31

Four test of significance were conducted on the same set of results: For test 1: alpha = 0.05, two-tailed test.
For test 2: alpha = 0.10, one-tailed test.
For test 3: alpha = 0.01, two-tailed test.
For test 4: alpha = 0.01, one-tailed test.
Which test is most likely to result in a rejection of the null hypothesis?

A) Test 1
B) Test 2
C) Test 3
D) Test 4

Question 32

When solving the formula for finding Z(obtained) with sample proportions in the two-sample case, we must first estimate

A) the standard deviation of the population
B) the population proportion
C) the ratio of the sample proportions
D) the critical region

Question 33

The higher the alpha level,

A) the lower the probability of rejecting the null hypothesis
B) the larger the sample size has to be to reject the null hypothesis
C) the greater the probability of rejecting the null hypothesis
D) the more desirable the two-tailed test

Question 34

When testing for the significance of the difference between sample means with small samples, the proper sampling distribution is

A) the alpha distribution
B) the beta distribution
C) the Z distribution
D) the t distribution

Question 35

From a university population, random samples of 45 seniors and 37 freshmen have been given a scale that measures sexual experiences. The freshmen report an average of 1.6 sexual partners over their lifetimes while seniors report an average of 2.5 partners. The t (obtained) for this difference was -3.56 while the t (critical) was $\pm$ 2.34. What can be concluded?

A) there is no significant difference between the classes
B) seniors and freshman are significantly different in their sexual experiences
C) freshman are more sexually active
D) sexual mores are deteriorating

Question 36

When testing hypotheses using two small samples, the t distribution may be used only after the additional assumption that

A) the populations means are equal
B) the population variances are equal
C) the population variances are not equal
D) the population means are different

Question 37

According to the text, tests of mathematical abilities of American boys and girls showed

A) no significant improvement between 2008 and 2012
B) a significant decrease in scores since 2008
C) a significant increase in scores since 2008
D) an increase in average scores for boy since 2008 but not for girls

Question 38

The lower the alpha level,

A) the lower the probability of rejecting the null hypothesis
B) the larger the sample size has to be to reject the null hypothesis
C) the greater the probability of rejecting the null hypothesis
D) the more desirable the two-tailed test

Question 39

A researcher conducted a survey to determine if older people have different feelings about abortion than younger people. He used an alpha level of 0.05 (Z critical = $\pm$ 1.96) to test for significance and found that his computed test statistic was 2.76. Which of the following conclusions is justified?

A) feelings about abortion do not vary by age
B) older and younger people have significantly different feelings about abortion
C) a one-tailed test should have been used
D) a Type II error has occurred

Question 40

When is the t distribution used instead of the Z distribution to test the significance of the difference between two sample proportions?

A) never
B) when sample size is very large
C) when one sample is much larger than the other
D) when N is small

Question 41

Random samples of 1546 men and 1678 women have been given a scale that measures support of legal abortion. Men average 12.45 and women average 12.46 and the difference is significant at the 0.05 level. What can we conclude?

A) There is an important difference between men and women on this issue.
B) Because of the large sample sizes, these results may be statistically significant but trivial.
C) The difference should be re-tested with a one-tailed test
D) The difference should be re-tested at a higher alpha level

Question 42

According to the text, which of the following is true regarding the gender gap in average income?

A) the gap has grown wider every year since the 1950s
B) the gap has grown smaller every year since the 1950s
C) the gap shrank to about 79% in 2012
D) the gap shrank to about 98% in 2012: a gender gap in income no longer exists

Question 43

Very large random samples of Catholics and Protestants have been questioned about their opinions on cohabitation. Forty-six percent of the Protestant and 47% of the Catholics approve of males and females living together without being married. The difference has been tested and found to be statistically significant. What is the most reasonable conclusion?

A) This is a statistically significant and important difference
B) This difference may be statistically significant but it seems unimportant
C) This difference is due to random chance
D) The researcher should have used sample means rather than proportions in this situation

Question 44

If a difference between random samples is not statistically significant, it is probably __________. On the other hand, a statistically significant difference is not necessarily ___________.

A) important … due to random chance
B) unimportant … large
C) important … unimportant
D) unimportant … important

Question 45

To maximize the probability of rejecting the null hypothesis, use

A) low alphas and two-tailed tests
B) low alphas and high Z scores
C) high alphas but low degrees of freedom
D) high alphas, large samples, and one- tailed tests

Question 46

The value of all test statistics increases as _______ increases

A) the sampling distribution
B) the alpha level
C) the size of the critical region
D) sample size

Question 47

According to information reported in the text, about 17% of men earn more than $100,000 a year vs. about ___% of women

A) 1
B) 3
C) 8
D) 10

Question 48

A difference between samples that is shown to be statistically significant is always

A) theoretically important
B) practically important
C) sociologically important
D) none of the above

Question 49

The larger the sample size, the

A) more important the observed difference
B) more likely we are to reject the null hypothesis
C) less likely we are to reject the null hypothesis
D) lower the Z score