Deck 8: Hypothesis Testing I: the One-Sample Case

Question 1

In tests of significance,if the test statistic does NOT fall in the critical region,we

A)conclude that the population distribution is normal.
B)reject the null hypothesis.
C)fail to reject the research hypothesis.
D)conclude that our alpha level was too low.

Answer 1

fail to reject the research hypothesis.

Question 2

The research hypothesis (H₁)typically states what the researcher expects to find and

A)contradicts the null hypothesis.
B)verifies on the null hypothesis.
C)modifies the null hypothesis.
D)is unrelated to the null hypothesis.

Answer 2

contradicts the null hypothesis.

Question 3

The null hypothesis in the one sample case is a statement of

A)agreement with the research hypothesis.
B)rejection.
C)acceptance.
D)no difference.

Answer 3

no difference.

Question 4

In tests of significance,if the test statistic falls in the critical region,we may conclude that

A)the population distribution is normal.
B)the null hypothesis can be rejected.
C)the research hypothesis is true.
D)our sample size was too small.

Question 5

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

A)if a sample is random.
B)if sample statistics are the same as those of the sampling distribution.
C)if parameters are representative of population.
D)if a sample came from a population with a certain characteristic.

Question 6

To conduct a test of hypothesis with a single sample mean,we must assume

A)the sampling distribution is normal.
B)random sampling.
C)interval-ratio level of measurement.
D)all of the above

Question 7

Like estimation procedures,hypothesis testing involves the risk that the sample

A)may not be representative.
B)may not be biased.
C)may be too large.
D)may not be significant.

Question 8

If the critical region begins at Z (critical)= $\pm$ 2.56 and the test statistic is -2.50,we

A)fail to reject the null hypothesis.
B)reject the null hypothesis.
C)cannot make a decision because the test statistic is so close to the critical region.
D)change the alpha level.

Question 9

Which assumption must be true in order to justify the use of hypothesis testing?

A)random sampling
B)interval-ratio level of measurement
C)very large samples
D)samples have been stratified

Question 10

In order to conduct a test of hypothesis with means or proportions,the sampling distribution must be

A)skewed.
B)large.
C)bimodal.
D)normal.

Question 11

Which of the following is NOT an assumption required for a test of hypothesis with a single sample mean?

A)a representative sample
B)sample size (N)larger than 1,000
C)normal sampling distribution
D)interval-ratio level of measurement

Question 12

In hypothesis testing,the ____ is the critical assumption,the assumption which is actually tested.

A)research hypothesis
B)null hypothesis
C)assumption of a normal sampling distribution
D)assumption that the sample was randomly selected

Question 13

All tests of hypothesis are based on the assumption that

A)the null hypothesis is false and should be rejected.
B)the observed difference is important.
C)the null hypothesis is true.
D)Type I errors are more serious than Type II errors.

Question 14

If we reject a null hypothesis of "no difference" at the 0.05 level,

A)the odds are 20 to 1 in our favor that we have made a correct decision.
B)the null hypothesis is true.
C)the odds are 5 to 1 in our favor that we have made a correct decision.
D)the research hypothesis is true.

Question 15

An alpha of 0.01 means that a decision to ____ the null hypothesis has a ____ in 100 chance of being incorrect

A)accept,1
B)fail to reject,1
C)reject,1
D)reject,100

Question 16

A sample of people attending a professional football game averages 13.7 years of formal education while the surrounding community averages 12.1.The difference is significant at the .05 level.What could we conclude?

A)the null hypothesis should be accepted
B)the research hypothesis should be rejected
C)the sample is significantly more educated than the community as a whole
D)the alpha level is too low

Question 17

Which of the following must be normally distributed in order to proceed with hypothesis testing of means and proportions?

A)the sample distribution
B)the sampling distribution
C)the population distribution
D)both the sample distribution and the population distribution

Question 18

Republicans average 1.4 children while the state as a whole averages 1.7 children.The Z scored computed in this test is 0.78 and the alpha level is 0.05.Therefore,the difference in size of family

A)is due to random chance.
B)does not reflect the situation of all Republicans.
C)is significant.
D)all of the above

Question 19

The research and null hypotheses ____ each other.

A)contradict
B)complement
C)amplify
D)rescind

Question 20

The critical region is

A)the area under the curve that contains "non-rare" events.
B)the area under the curve that includes those values of a sample statistic that will lead to rejection of the null.
C)a confidence interval.
D)a law that states that the shape of the sampling distribution is normal.

Question 21

The probability of Type I error is

A).01.
B).05.
C)the alpha level.
D)beta.

Question 22

Which of the following combinations would result in a Type I error? The null hypothesis is actually ____ and our decision in Step 5 is to ____ the null hypothesis.

A)false,fail to reject
B)false,reject
C)true,fail to reject
D)true,reject

Question 23

If we reject a null hypothesis which is in fact true,we

A)have made a correct decision.
B)have made a Type I error.
C)have made a Type II error.
D)should have used a one-tailed test.

Question 24

In a t test of differences between means,increasing sample size will affect

A)degrees of freedom.
B)standard deviation of the sampling distribution.
C)t score.
D)all of the above

Question 25

Do sex education classes and free clinics that offer counseling for teenagers reduce the number of pregnancies among teenagers? The appropriate test of hypothesis would be

A)a one-tailed test.
B)a two-tailed test.
C)cross-sectional.
D)participant observation.

Question 26

A one-tailed test of significance could be used whenever

A)the researcher can predict a direction for the difference.
B)the researcher feels like it.
C)the null hypothesis is thought to be true.
D)the alpha level exceeds 0.10.

Question 27

Comparing one- and two-tailed tests (with a constant alpha level and sample size),the probability of rejection will be higher for

A)the two-tailed test.
B)the one-tailed test,if you have correctly predicted the direction of the difference.
C)neither,the probability of rejection does not change.
D)the test with the most conservative test statistic.

Question 28

With alpha set at .05,the Critical Region for a two-tailed test would begin at $\pm$ 1.96.In a one-tailed test at the same alpha level,the Critical Region would begin at

A) $\pm$ 1.96.
B) $\pm$ 2.58.
C) $\pm$ 2.30.
D) $\pm$ 1.65.

Question 29

When we decide on a value for alpha,we are

A)defining the likelihood of accepting the alternative hypothesis.
B)establishing whether the test will be one or two tailed.
C)setting the probability of committing a Type I error.
D)setting the probability of a one-tailed test.

Question 30

Which of the following are we unlikely to know when conducting a test of hypothesis in the one sample case?

A)the sample standard deviation
B)the mean of the sample
C)the standard deviation of the population
D)the alpha level

Question 31

All other things being equal,with which of the following alpha levels would we be most likely to reject the null hypothesis?

A).01
B).001
C).05
D).10

Question 32

Given that the null hypothesis is actually true,the probability of Type II error is

A).00.
B).05.
C)1.00.
D)the alpha level.

Question 33

Which of the following combinations would result in a Type II error? The null hypothesis is actually ____ and our decision in Step 5 is to ____ the null hypothesis.

A)false,fail to reject
B)false,reject
C)true,fail to reject
D)true,reject

Question 34

As the Critical Region decreases in size,

A)the probability of Type I error increases.
B)the probability of rejecting the null hypothesis increases.
C)alpha increase.
D)the probability of Type II error increases.

Question 35

In a one-tailed test of hypothesis,the entire ____ should be placed in either the upper or lower tail of the ____.

A)critical area,sampling distribution
B)sample mean,population distribution
C)Z score,critical area
D)sampling distribution,sample distribution

Question 36

The t distribution,compared to the Z distribution,is

A)more skewed.
B)more peaked for small samples but increasingly like the Z distribution as N increases.
C)bimodal.
D)flatter for small sample sizes but increasingly like the Z distribution as N increases.

Question 37

The higher the alpha level,the more likely we will

A)commit a Type I error.
B)commit a Type II error.
C)conduct a two-tailed test.
D)be unable to decide whether to reject or fail to reject the null hypothesis.

Question 38

A researcher is investigating an outreach program that is intended to reduce the number of homeless children in the state.In this situation,it would be appropriate to use a ____ test of significance

A)random.
B)non-probability.
C)one-tailed.
D)zero alpha.

Question 39

Given the same alpha level,the one-tailed test

A)makes it harder to reject the H₀.
B)does not affect the probability of rejecting the H₀.
C)makes it more likely that H₀ will be rejected.
D)is less dependable than the two-tailed test.

Question 40

A researcher is interested in the effect that neighborhood crime-watch efforts have on the crime rate in the inner city,but he is unwilling to predict the direction of the difference.The appropriate test of hypothesis would be

A)one-tailed.
B)two-tailed.
C)descriptive.
D)symmetrical.

Question 41

Sixty percent of the respondents in a random sample drawn from a neighborhood are Democrats.The community as a whole is 75% Democrat.The difference between sample and population has been tested and the null hypothesis has been rejected.What may we conclude?

A)a Type I error has been committed
B)a one-tailed test has been used
C)the neighborhood is significantly less likely to be Democrat
D)the difference is not significant

Question 42

When testing for the significance of the difference between a sample mean and a population mean,degrees of freedom are equal to

A)N - 1.
B)N + 1.
C)alpha.
D)1 - alpha.

Question 43

The records of the state Division of Motor Vehicles reveals that 23% of all drivers have been ticketed at least once.Twenty-five percent of a random sample of older drivers in the state have gotten at least one ticket.This difference has been tested and the researcher has failed to reject the null hypothesis.What can be concluded?

A)Older drivers are better drivers.
B)Older drivers are worse drivers.
C)There is no significant difference between older drivers and drivers in general in terms of number of tickets.
D)Older drivers are significantly different from drivers in general.

Question 44

A researcher selected a sample of 56 former student leaders from a list of graduates of a large university.She discovered that it had taken an average of 4.97 years for these graduates to finish their degrees,with a standard deviation of 1.23.The average for the entire student body is 4.56 years.Is the difference statistically significant? Follow the five-step model and state all important decisions.Make sure that you interpret the results in terms of the original research question.

Question 45

If the test statistic does not fall in the critical region,we

A)reject the null hypothesis.
B)fail to reject the null hypothesis.
C)lower the alpha level and conduct a new test.
D)commit a Type I error.

Question 46

In your own words,define and explain each of the following terms and concepts:

A)the null hypothesis
B)Type I (alpha) error
C)Sampling distribution
D)One-tailed test

Question 47

Under what condition might we use proportions rather than means as the test statistic?

A)when sample size is very small
B)when sample size is very large
C)when the variable of interest is only interval-ratio in level of measurement
D)when the variable of interest is only nominal in level of measurement

Question 48

Do students who are members of fraternities or sororities have GPAs different from the student body as a whole? A random sample of 123 "Greeks" has been selected from the student body of a large university.The GPA for the student body as a whole is 2.59 and the mean for the sample is 2.47 with a standard deviation of 0.34.Is the difference statistically significant? Follow the five-step model and state all important decisions.Make sure that you interpret the results in terms of the original research question.

Question 49

If the test statistic falls in the critical region,we

A)reject the null and conclude that the research hypothesis is true.
B)reject the null and conclude that there is strong -- although indirect -- support for the research hypothesis.
C)accept the null.
D)fail to reject the null.

Question 50

From a random sample of size 200 drawn from a local community,120 respondents identify themselves as Democrats.For the community as a whole,75% of the residents classify themselves as Democrats.In this research situation

A)P_s is .60 and P_u is .50.
B)P_u is .75 and P_s is .60.
C)P_u is .75 and P_s is 120.
D)the t test is called for.

Question 51

When testing a single sample mean for significance when the population standard deviation is unknown and sample size is 75,the correct sampling distribution is

A)the t distribution.
B)the Z distribution.
C)it makes no difference.
D)t for a one-tailed test,Z for a two-tailed test.

Question 52

In order to reject the null hypothesis when using the t distribution and small samples,we will

A)need a smaller test statistic as compared to larger samples.
B)need a larger test statistic as compared to larger samples.
C)always use one-tailed tests.
D)set alpha very low.

Question 53

Cite an example of a research situation in which a one-tailed test of significance would be appropriate.

Question 54

A researcher selected a sample of 268 former student athletes from a list of graduates of a large university.A total of 17% of the sample of athletes had earned graduate degrees as compared 14% of all graduates.Is the difference statistically significant? Follow the five step model and state all important decisions.Make sure that you interpret the results in terms of the original research question.

Question 55

Under what conditions would you use the t distribution to test the significance of a single sample proportion?

A)none,use the Z distribution as long as sample size is large
B)only when the population standard deviation is known
C)only when sample size is less than or equal to 120
D)only when the population is normally distributed