Deck 8: Hypothesis Testing I the One Sample Case

Question 1

Republicans average 1.4 children while the state as a whole averages 1.7 children. The Z score 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 answer choices

Answer 1

A

Question 2

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.

Answer 2

B

Question 3

Research involving potentially harmful drugs would be likely to use an alpha level of________.

A) 0.10
B) 0.075
C) 0.05
D) 0.001

Answer 3

D

Question 4

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 5

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 6

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 answer choices

Question 7

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 8

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 increases.
D) the probability of Type II error increases.

Question 9

Given the same alpha level, the one-tailed test________.

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

Question 10

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 11

In terms of hypothesis testing, "significance" refers to the________.

A) difference between an independent and dependent variable.
B) difference between the sample and population values.
C) difference between the two independent variables.
D) difference between our observed and our predicted outcomes.

Question 12

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

A) ± 1.96.
B) ± 2.58.
C) ± 2.30.
D) ± 1.65.

Question 13

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

A) 0.00
B) 0.05
C) 1.00
D) the alpha level.

Question 14

Why would researchers use the t distribution?

A) The population standard error is usually unknown.
B) It is best for larger samples.
C) It always has more accurate results.
D) The Z distribution is always preferable.

Question 15

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

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

Question 16

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 17

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 18

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 19

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 20

If the critical region begins at Z (critical) =±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 21

To calculate degrees of freedom, a researcher uses which formula?

A)
B)
C)
D)

Question 22

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 23

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 24

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 25

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 26

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.

Question 27

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 28

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 29

A professor wants to determine if the grades in her introductory criminal justice class were higher than the rest of the school. With a total of 101 students in her class, they had a mean exam grade of 87, and a standard deviation of 3. She was not able to obtain the standard deviation for the other introductory classes, but the mean grade of all classes was 74. Which of the following would be the test statistic used, and what is the correct answer?

A) t = 0.39
B) t = 0.43
C) Z = 0.39
D) Z = 0.43

Question 30

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 31

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 32

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 answer choices

Question 33

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 34

From a random sample size of 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 35

The research hypothesis (H 1) 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.

Question 36

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 37

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.