Deck 8: Hypothesis Testing

Question 1

In hypothesis testing, if we obtain a sample mean that is larger than the population mean,

A) we can reject the null hypothesis.
B) we can reject the alternative hypothesis.
C) the difference could be due to random sampling error.
D) we can conclude that our treatment was effective.

Answer 1

C

Question 2

Step 2 of the hypothesis testing procedure instructs us to

A) calculate the relevant statistics.
B) indicate the alpha level and determine critical values.
C) formulate our hypotheses.
D) make a decision and report the results.

Answer 2

B

Question 3

We use hypothesis testing to

A) estimate the characteristics of a population based on sample data.
B) estimate the characteristics of a sample based on information from the population.
C) prove the alternative hypothesis to be wrong.
D) prove the null hypothesis to be right.

Answer 3

A

Question 4

If there is a difference between the population mean and our obtained sample mean, the alternative hypothesis states that the difference is due to

A) chance.
B) the effect of the independent variable.
C) random sampling error.
D) ineffective treatment.

Question 5

Hypothesis testing is based on the assumption that

A) the null hypothesis is true.
B) the null hypothesis is false.
C) the independent variable will be effective.
D) differences between μ and M are true differences, rather than chance differences.

Question 6

Step four of the hypothesis testing procedure involves

A) stating the hypothesis.
B) determining critical values.
C) calculating the statistics.
D) making a decision and reporting the results.

Question 7

If the mean of a population is 10, which of the following is not a correctly stated null hypothesis for a z-test?

A) H₀: μ ≥ 10
B) H₀: μ = 10
C) H₀: μ ≠ 10
D) H₀: μ ≤ 10

Question 8

If the mean of a population is 25, which of the following is not a correctly stated alternative hypothesis for a z-test?

A) H₁: μ ≤ 25
B) H₁: μ > 25
C) H₁: μ ≠ 25
D) H₁: μ < 25

Question 9

In hypothesis testing if a significant effect is found, you should

A) do nothing.
B) reject the alternative hypothesis.
C) fail to reject the null hypothesis.
D) reject the null hypothesis.

Question 10

A non-directional alternative hypotheses for a z-test can be represented as

A) H₁: μ ≤ 60.
B) H₁: μ ≠ 60.
C) H₁: μ ≥ 60.
D) either "a" or "c" above.

Question 11

In hypothesis testing, researchers usually want to

A) reject H₁.
B) obtain support for H₀.
C) reject H₀.
D) fail to reject H₀.

Question 12

Which of the following statements about the alpha level is NOT true?

A) It is a probability level.
B) It is a population parameter.
C) It defines the point at which H₀ should be rejected.
D) It defines the point at which the critical region begins.

Question 13

In hypothesis testing, H₀ states that

A) obtained differences from μ are more than chance differences.
B) the independent variable was effective.
C) the independent variable was not effective.
D) both "a" and "b" are correct.

Question 14

The score that marks the beginning of the rejection area in a sampling distribution is the

A) obtained z-score.
B) obtained sample mean.
C) population mean.
D) critical value.

Question 15

In conducting a z-test with a nondirectional alternative hypothesis, we would

A) use a two-tailed test.
B) use a one-tailed test.
C) not divide the alpha level in two.
D) both "b" and "c" are correct.

Question 16

Obtained sample values that fall in the rejection region of a sampling distribution

A) have a high probability of occurrence if H₀ is true.
B) have a low probability of occurrence if H₀ is true.
C) suggest that the independent variable was effective.
D) both "b" and "c" are true.

Question 17

If we are using a nondirectional alternative hypothesis for a z-test with α = .05, what critical value(s) should be used for rejecting the null hypothesis?

A) -1.96 only or +1.96 only.
B) +1.65 only or -1.65 only.
C) either ±1.96
D) either ±1.65

Question 18

If we are using a directional alternative hypothesis for a z-test with α = .01, what critical value(s) should be used for rejecting the null hypothesis?

A) -2.33 only or +2.33 only.
B) either ±2.33
C) -2.58 only or +2.58 only.
D) either ±2.58.

Question 19

It is more difficult to reject H₀

A) with a one-tailed test.
B) with a two-tailed test.
C) with α = .05 rather than .01.
D) with α = .01 rather than .001.

Question 20

The rejection region of a sampling distribution is determined by ______.

A) H₀
B) H₁
C) α
D) z

Question 21

If we fail to reject H₀,

A) we have gained support for our alternative hypothesis.
B) the evidence does not show that treatment was effective.
C) the evidence suggests that treatment was effective.
D) our obtained value had a low probability of occurrence.

Question 22

A study resulted with a z_obt = +2.34. z_crit was ±2.03 with α = .05. Based on these results,

A) we should fail to reject H₀.
B) we should reject H₁.
C) p > .05
D) p < .05

Question 23

In statistical terminology, the term "significant" in the results section

A) indicates a greater than chance result.
B) suggests that the result is likely due to chance.
C) suggests that we should fail to reject H₀.
D) suggests a high probability of occurrence.

Question 24

If research results support the alternative hypothesis, we would

A) fail to reject H₀.
B) reject H₁.
C) reject H₀.
D) both "a" and "b" are correct.

Question 25

If the alpha level is set at .01, then a p < .01

A) suggests a significant result.
B) suggests a non-significant result.
C) means that we should reject H₀.
D) both "a" and "c" are true.

Question 26

If our obtained sample mean ended up in the rejection region of a sampling distribution,

A) the z_crit would be greater than z_obt.
B) the probability level would be greater than alpha.
C) it would have had low probability of occurrence if H₀ were true.
D) both "a" and "b" are correct.

Question 27

Effect size indicates

A) the magnitude of a treatment effect.
B) when to reject the null hypothesis.
C) the probability associated with our obtained sample data.
D) the value of z_crit.

Question 28

Using Jacob Cohen's guidelines for interpreting the size of an effect, d = .74 would indicate

A) a small effect.
B) a moderate effect.
C) a large effect.
D) an extra large effect.

Question 29

An effect size of d = .75 is equivalent to

A) where 75% of the sample means will fall.
B) a probability level of the same value.
C) three-fourths of the critical value.
D) three-fourths of a standard deviation.

Question 30

Given z_crit = -2.33, which of the following obtained z-values will result in rejecting the null hypothesis?

A) z_obt = +2.40
B) z_obt = -2.40
C) z_obt = +2.09
D) z_obt = -2.09

Question 31

Given z_crit = ±2.58, which of the following obtained z-values will result in rejecting H₀?

A) -3.01
B) +2.54
C) +2.93
D) either "a" or "c" will reject H₀.

Question 32

If z_crit = ±2.33 and z_obt = +2.12, the correct statistical decision would be to ______________.

A) retain H₁
B) fail to reject H₁
C) reject H₀
D) fail to reject H₀

Question 33

Assume z_crit = +1.65 with α = .05 and z_crit = +2.33 with α = .01. Assume further that z_obt = +2.02. The correct statistical decision would be to

A) fail to reject H₀ at both α = .05 and α = .01.
B) reject H₀ at both α = .05 and α = .01.
C) reject H₀ at α = .05 but fail to reject H₀ at α = .01.
D) reject H₀ at α = .01 but fail to reject H₀ at α = .05.

Question 34

Which of the following alpha levels will make it more difficult to reject H₀?

A) .001
B) .01
C) .02
D) .05

Question 35

If the results of a hypothesis test include the phrase "p > .05," then the decision should be made to ____________.

A) reject H₀.
B) fail to reject H₀.
C) accept H₁.
D) both "a" and "c" are true.

Question 36

If you are using a two-tailed z-test, ________ is divided in half.

A) α
B) z_crit
C) σ_M
D) z_obt

Question 37

Which of the following is not one of the assumptions for the z-test?

A) A normal population distribution.
B) σ is unknown.
C) Independent and random selection of subjects.
D) Interval or ratio scores.

Question 38

Procedures that test hypotheses about populations are called

A) parametric tests.
B) statistical tests.
C) empirical tests.
D) descriptive statistics.

Question 39

According to Jacob Cohen's guidelines for interpreting effect size, d-values that fall in the range of __________ represent a small effect.

A) .00 to .20
B) .10 to .20
C) .20 to .49
D) .10 to .30

Question 40

If we make a Type I error, then we have

A) rejected a false H₀.
B) rejected a true H₀.
C) accepted a false H₀.
D) accepted a true H₁.

Question 41

If we have committed a Type II error, we have

A) used the wrong alpha level.
B) claimed a treatment to be effective when it wasn't.
C) failed to recognize a treatment that was effective.
D) rejected a null hypothesis that was actually true.

Question 42

Which of the following alpha levels would have the lowest risk of a Type I error?

A) .05
B) .02
C) .01
D) .001

Question 43

Which of the following alpha levels would have the greatest risk of a Type II error?

A) .05
B) .02
C) .01
D) .001

Question 44

If there were serious consequences of making a Type I error, which alpha level would you choose?

A) .05
B) .02
C) .01
D) .001

Question 45

A researcher is on the verge of a breakthrough for a medical procedure that has little risk but that could be of great benefit to patients. What alpha level should she choose?

A) .05
B) .02
C) .01
D) .001

Question 46

The population mean of a standardized test on Cheerfulness is 50. An attitude coach who conducts self-improvement workshops administered the test to a sample of his participants. The obtained sample mean was 55. Since the obtained sample mean was 5 points higher than the population mean can we, therefore, conclude that the workshop was effective? Why or why not?

Question 47

Assume a study is being conducted to determine if a sample mean would be significantly different from the population mean of 35. Write the symbolic notation for both the null and alternative hypotheses for
a. a nondirectional test, and
b. a directional test that specifies that the treatment will improve scores.

Question 48

Explain why obtained sample values that fall in the critical region of a sampling distribution result in rejection of the null hypothesis.

Question 49

Is it easier to reject a null hypothesis with a one-tailed test or a two-tailed test? Explain.

Question 50

If our obtained sample mean falls in the critical region of a sampling distribution, have we gained support for H₀ or H₁? Explain.

Question 51

Explain what is meant by Type I error. How can researchers reduce the risk of making such an error?

Question 52

Explain what is meant by the power of a statistical test. What are the factors that increase power?

Question 53

One of the founders of a society for skeptics believes that people would benefit from a more questioning attitude about various claims that people make and he has developed a course to teach such skills. A standardized skepticism assessment has a μ = 90 and a σ = 20. A sample of n = 40 is obtained from students who have taken his course and their mean is M = 99.
a. Employ the four-step hypothesis testing procedure to determine the effectiveness of the course using a two-tailed z-test and an α = .01.
b. If a significant difference was found, determine the size of the effect.

Question 54

Balance disturbances can be a common source of difficulty for senior citizens. One type of balance test involves standing on one leg, arms crossed and eyes open. The population mean for females, aged 60 - 69, on the balance test is 30 seconds with a σ = 5 seconds. A fitness instructor is implementing a program at her facility, which she calls "Toe the Line," designed to improve balancing skills. After completing the program, a sample of 15 females in the 60 - 69 age group take the balance test. The mean for the sample was M = 32. Using a one-tailed z-test and α = .05, determine whether the program improved balancing skills in older females.