Deck 9: The Z-Test

Question 1

The trial of the Pyx illustrates the concept of random sampling but not the concept of hypothesis testing.

Answer 1

False

Question 2

In general, as the size of an effect decreases, the mean of the observed sample will be closer to the mean of the theoretical null population.

Answer 2

True

Question 3

The value that is most likely to occur in a sampling distribution of means is the sample mean.

Answer 3

True

Question 4

The magnitude of the effect of an independent variable on the dependent variable is unrelated to the distance of the sample mean from the mean of the sampling distribution.

Question 5

The effect size is a measure that assumes that the null hypothesis is true.

Question 6

The p-value is a measure of probability that assumes that the alternative hypothesis is true.

Question 7

The effect size and p-value are both examples of non-conditional probability.

Question 8

In hypothesis testing, if observed scores fall within the acceptance region, then you can accept the alternative hypothesis.

Question 9

In hypothesis testing, the rejection region will always have a smaller area than the rest of the distribution.

Question 10

If the observed z-score is larger than critical z, then we should always reject the null hypothesis.

Question 11

Critical z is a value that is determined solely by the design of the study and not by the observed data.

Question 12

In hypothesis testing, the rejection region is an area and a proportion and also a probability.

Question 13

In a study with a non-directional hypothesis, there are two rejection regions within the same distribution.

Question 14

The alpha level is the actual size of the area/s that correspond to the rejection region.

Question 15

In the field of psychology, the conventional choice of alpha for hypothesis testing is 0.1.

Question 16

Imagine that you hypothesize that students will complete a test more quickly if they take the test in cold room than in a warm room. If the critical z of a test is -2.33 and you obtain a z-statistic of 1.2, you should reject the null hypothesis.

Question 17

No matter how small the p-value is, there is always the chance that your data was obtained as a result of random error.

Question 18

The decision to reject a null hypothesis that is actually true is known as Type I error.

Question 19

The decision not to reject a null hypothesis that is actually false is known as Type II error.

Question 20

Choosing a smaller alpha level is one way to reduce the risk of committing a Type I error.

Question 21

In the trial of the Pyx…

A) The coins in the Pyx had to be significant different from each other.
B) The coins in the Pyx were specially chosen to be the purest that could be found.
C) The Central Limit Theorem was violated.
D) None of the above.

Question 22

In a normal distribution…

A) A value that is far from the mean is more likely to occur than a value that is closer to the mean.
B) All values are equally likely to occur.
C) A negative value is less likely to occur than a positive value.
D) Values at the tail ends are less likely to occur than the mean.

Question 23

Eileen hypothesizes that a new therapy for phobia will improve wellbeing scores of her clients. Assuming that her null hypothesis is true…

A) She is more likely to obtain a sample mean that is positive than a sample mean that is negative.
B) She is more likely to obtain a sample mean that is negative than a sample mean that is positive.
C) She is more likely to obtain a sample mean that is more than two standard deviations higher than the population mean than a sample mean that is within one standard deviation of the population mean.
D) She is more likely to obtain a sample mean that is within one standard deviation of the population mean than a sample mean that is more than two standard deviations higher than the population mean.

Question 24

Esther is comparing the results of two studies. Both studies use the same independent and dependent variables and have the same sample size. If Study 1 reports a larger effect size than Study 2…

A) Study 1 has an observed sample mean that is closer to the mean of the sampling distribution than Study 2.
B) Study 1 has an observed sample mean that is further away from the mean of the sampling distribution than Study 2.
C) Study 1 has more variability than Study 2.
D) Study 2 has more variability than Study 1.

Question 25

Arlene has conducted an experiment examining the effect of sleep on time spent procrastinating in students. She found that the fewer hours of sleep students had, the more they procrastinated on completing an assignment. The magnitude of the influence of sleep on procrastination is called:

A) The p-value
B) The alternative hypothesis
C) The effect size
D) The population mean

Question 26

Which of the following is true of the rejection region in hypothesis testing?

A) It is an outer region in a sampling distribution of means. If the critical value of z falls in this area, you can conclude that your sample mean is significantly different from the population mean.
B) It is a middle region in a sampling distribution of means. If the critical value of z falls in this area, you can conclude that your sample mean is significantly different from the population mean.
C) It is an outer region in a sampling distribution of means. If the observed value of z falls in this area, you can conclude that your sample mean is significantly different from the population mean.
D) It is a middle region in a sampling distribution of means. If the observed value of z falls in this area, you can conclude that your sample mean is significantly different from the population mean.

Question 27

Which of the following statements is true about critical z?

A) Critical z is a probability that spans the rejection area in the sampling distribution.
B) Critical z is a standardized value that is determined by the chosen alpha level.
C) Critical z is an unstandardized value that is determined by the chosen sample size.
D) Critical z is a probability that is the same as the p-value of a test.

Question 28

In a study with a non-directional hypothesis…

A) There is a single rejection region with an area that corresponds to the alpha level.
B) There is a single rejection region with an area that corresponds to the p-value.
C) There are two rejection regions that have the same area that adds up to the alpha level.
D) There are two rejection regions that have the same area that adds up to the p-value.

Question 29

Alexa hypothesizes that consuming whole-grain cereal for breakfast will cause students to take part in more exercise throughout the day. Assuming that she chooses an alpha level of .05, what is the critical z of her test?

A) -1.65
B) +1.65
C) -1.96
D) +1.96

Question 30

Assuming that the null hypothesis is true, how likely does it have to be for a sample mean to be observed before a researcher can make the decision to reject the null hypothesis?

A) 1%
B) 5%
C) 0.1%
D) 10%

Question 31

Which of the following statements about the alpha level is false?

A) The alpha level can be set to be smaller than 5% but not larger than 5%.
B) The alpha level is decided upon before calculating the p-value of a test.
C) The alpha level is a convention set by mutual agreement amongst researchers.
D) The alpha level is unrelated to the sampling distribution of the mean.

Question 32

The p-value and the alpha level are both…

A) always positive
B) not expressions of probability
C) calculated from the observed data
D) mutually exclusive

Question 33

Which of the following statements is not true of the p-value?

A) It is the conditional probability of an outcome happening by chance.
B) It is used to make a dichotomous decision in hypothesis testing.
C) It is obtained from the observed sample.
D) None of the above.

Question 34

Critical z is to the z-statistic as…

A) The sample mean is to the population mean
B) The population mean is to the sample mean
C) The alpha level is to the p-value
D) The p-value is to the alpha level

Question 35

If the critical z of a test is $\pm$ 1.96, what inferences can you make about other aspects of the test?

A) The hypothesis is directional and the alpha level is .01
B) The hypothesis is directional and the alpha level is .05
C) The hypothesis is non-directional and the alpha level is .01
D) The hypothesis is non-directional and the alpha level is .05

Question 36

Veronica obtains a z-score of -1.16 from her study that has an alpha level of .05. Which of the following must be true?

A) If she has a directional hypothesis, she will be able to reject the null hypothesis.
B) If she has a non-directional hypothesis, she will be able to reject the null hypothesis.
C) Her obtained z-score is not within the rejection region.
D) Her obtained z-score is smaller than critical z.

Question 37

If you have an experimental manipulation that you hypothesize will decrease scores, then for you to be able to reject the null hypothesis, your observed z-score must be:

A) Negative
B) Positive
C) Zero
D) There is insufficient information to make conclusions about the z-score.

Question 38

Which of the following is true about hypothesis testing?

A) If your observed mean does not fall in the rejection region, you can choose not to make a conclusion.
B) You can change the alpha level after calculating the p-value to make the reasons for your decision to reject the null hypothesis more persuasive.
C) Despite random sampling and doing all the steps in hypothesis testing correctly, it is possible to make a wrong conclusion.
D) None of the above

Question 39

The decision to reject a true null hypothesis is called _________ while the decision to accept a false null hypothesis is _________.

A) Type I error; Type II error
B) Type I error; a correct decision
C) A correct decision; Type I error
D) Type II error; Type I error

Question 40

A scientist decides to accept the null hypothesis when the alternative hypothesis is false. The scientist has made:

A) A Type I error
B) A Type II error
C) A correct decision
D) A sampling error

Question 41

Which method can be taken by the scientist that will end up increasing the risk of Type I error?

A) Decreasing the p-value
B) Decreasing the alpha level
C) Increasing the sample size
D) Increasing the population mean

Question 42

Type I error can be reduced by…

A) Choosing a directional hypothesis
B) Decreasing the alpha level
C) Increasing the sample size
D) None of the above

Question 43

Since there are several ways of reducing Type I error, why do researchers not always choose to use all the possible ways to do so? Select the option that is the best reason.

A) Type I error it is actually a good thing because it helps researchers to make important discoveries.
B) Researchers cannot always choose to use a directional hypothesis to reduce Type I error because sometimes they do not know which direction the effect will take.
C) Taking steps to reduce Type I error may increase the risk of Type II error.
D) Researchers are usually more focused on reducing Type II error and are willing to increase Type I error to do so.

Question 44

Bennett is trying to reduce the chances of mistakenly concluding that there is an effect of his independent variable when there actually is not. What error is he trying to reduce?

A) Measurement error
B) Type I error
C) Type II error
D) Type III error

Question 45

Melissa is trying to reduce the probability of missing a true effect of her independent variable. She is trying to reduce:

A) Measurement error
B) Type I error
C) Type II error
D) Type III error

Question 46

Claire conducts a study on the effects of stress and eating candy. She hypothesizes that increased feelings of being stressed will cause students to eat more candy. Assuming that she uses an alpha level of .05, draw and shade the rejection region of Claire's study. Label the position of the critical z. What is the probability of Claire's observed data being in the rejection region, assuming that the null hypothesis is true?

Question 47

If the z-score of Julio's test is -0.9, what proportion of values in a normal distribution would lie above this value? Illustrate the area in the standard normal distribution that corresponds to your answer.

Question 48

Define Type I and Type II error. List a way of reducing Type I error and a way of reducing Type II error.

Question 49

In Zoey's study, she has obtained a sample mean of 10. She would like to compare it to the population, to find out if her sample is significantly different.
Given that the population mean is 9 and the population standard deviation is 0.45, what is the z-value of her test?

Question 50

In Zoey's study, she has obtained a sample mean of 10. She would like to compare it to the population, to find out if her sample is significantly different.
Assuming that the alpha level is .05, should her null hypothesis be rejected or retained?

Question 51

Greg wants to find out if he did better than Steve in music class. Greg received a score of 80 in his music class, where the mean score was 76 and the standard deviation was 7. Steve received a score of 34 in his music class, where the mean score was 30 and the standard deviation was 5.
Did Greg perform relatively better than Steve?

Question 52

Greg wants to find out if he did better than Steve in music class. Greg received a score of 80 in his music class, where the mean score was 76 and the standard deviation was 7. Steve received a score of 34 in his music class, where the mean score was 30 and the standard deviation was 5.
Did Greg perform relatively better than Steve?
How do you know?