Deck 9: Hypothesis Testing II: the Two-Sample Case

Question 1

When conducting hypothesis tests for two sample means,the term m₁ - m₂ 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.

Answer 1

the null hypothesis is assumed to be true.

Question 2

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.

Answer 2

sample standard deviations corrected for bias.

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

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 5

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 6

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 7

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

Question 8

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 9

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 (a > 0.10)is called for

Question 10

To satisfy the requirement of independent random sampling,the researcher

A)must use only cluster 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 11

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 12

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 13

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 14

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 15

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

A) $\bar { X } _ { 1 } = \bar { X } _ { 2 }$
B)m > 0.
C)m = m.
D)s = s.

Question 16

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 17

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 $\pm$ 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 18

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 19

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 20

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

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

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 24

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 25

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 26

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.

Question 27

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 28

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 29

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 30

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 31

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 32

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 33

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 34

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 35

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 36

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

A)P_s1 = P_s2.
B)P_s1 = P_s21.
C)P_u = (1 - P_u).
D)P_u1 = P_u2.

Question 37

Four tests 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 38

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 39

From a university population,random samples of 45 seniors and 37 freshman have been given a scale that measures sexual experiences.The freshman 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 40

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 41

A sample of students attending a large university has been selected.Is there a statistically significant difference between Liberal Arts majors and other students on average number of books (other than those required by course work)read per year? Use the five step model and write a sentence or two interpreting your results.

Question 42

The text reports the results of a test for the significance of the difference in average income for random samples of males and females.Males earned an average of about $17,000 more per year and the Z score computed in step 4 was 10.18.Given these results,which of the following is a reasonable conclusion?

A)The difference is statistically significant,large,and important.
B)The difference is not statistically significant and was probably caused by random chance.
C)There is no gender gap in income in the United States.
D)This difference is statistically significant but quite small.

Question 43

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 44

The text reports the results of a test for the significance of the difference in average education for random samples of males and females.Males earned an average of 13.35 years of schooling and females averaged 13.25 years.The Z score computed in step 4 for this difference was 1.02.Given these results,which of the following is a reasonable conclusion?

A)The difference is statistically significant,large,and important.
B)The difference is not statistically significant and was probably caused by random chance.
C)There is an important gender gap in education in the United States.
D)This difference is statistically significant but quite small.

Question 45

A scale measuring confidence in the media was administered to a sample.Is there a statistically significant difference between Democrats and Republicans on the scale? Higher scores on the scale indicate greater confidence.Use the five step model and write a sentence or two interpreting your results.

Question 46

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 47

Is there a statistically significant difference between males and females in terms of newspaper readership? The proportion of each sex that says they read a newspaper daily is reported below.Results are from a nationally representative sample.Use the five step model and write a sentence or two interpreting your results.

Question 48

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 49

What causes the gender gap in income documented in the text? One possible reason is that

A)men and women hold different kinds of careers and jobs.
B)women are much less educated than men.
C)women have much higher rates of unemployment than men.
D)all of the above

Question 50

Which of the following was true for the test for differences in average education by gender reported in the text?

A)the information on education came from the U.S.Bureau of the Census
B)the average years of education for males was almost twice that of females
C)the test was based on very small samples of less than 100 females and males
D)the information on education came from the 2006 General Social Survey

Question 51

Which of the following was true for the test for differences in average income by gender reported in the text?

A)the information on income came from the U.S.Bureau of the Census
B)the income of males,on the average,was almost twice that of females
C)the test compared only people who worked full time
D)the test compared only people who had a least a high school education

Question 52

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 53

Comparing gender differences in average education with differences in average income,we found

A)large and significant gender differences in education but no difference in income.
B)no significant gender difference on either variable.
C)large and significant gender differences in income but no difference in education.
D)large and significant gender differences in both education and income.