Deck 7: Testing Differences Between Means

Question 1

Compared to the .05 level of significance, the .01 level of significance means:

A)a higher probability of the obtained difference being a result of sampling error.
B)a lower probability of the obtained difference being a result of sampling error.
C)a perfectly normal distribution.
D)a skewed distribution.

Answer 1

a lower probability of the obtained difference being a result of sampling error.

Question 2

When the null hypothesis is rejected:

A)it is quite likely that the difference between means is a result of sampling error.
B)the research hypothesis is proven false.
C)it is unlikely that the difference between means is a result of sampling error.
D)the population means are equal.

Answer 2

it is unlikely that the difference between means is a result of sampling error.

Question 3

The question below refers to the following situation:
A researcher is interested in the relationship between political party affiliation (Democrat Or Republican) and support for a woman's right to choose (Pro-Choice). In order to do this She uses a standardized measure for determining support for Pro-Choice. The higher the Person scores on the measure, the greater is his or her support for Pro-Choice.
If the researcher claims a significant difference between groups, when in fact none exists:

A)a Type 1 error has been made.
B)a Type 2 error has been made.
C)the null hypothesis was correctly retained.
D)the research hypothesis was correctly rejected.

Answer 3

a Type 1 error has been made.

Question 4

Which of the following exemplifies a research hypothesis?

A)Men and women have different levels of income.
B)White and African Americans watch the same amount of TV.
C)Senior citizens driving behaviors do not differ from those of teenagers.
D)Liberals and conservatives have the same voting rates.

Question 5

If we retain a null hypothesis that is in fact false:

A)we have committed a Type 1 error.
B)we have committed a Type 2 error.
C)we have claimed a difference when none exists in the population.
D)we have miscalculated the difference between sample means.

Question 6

As β (beta) decreases:

A)the probability of making a Type 2 error increases.
B)the probability of making a Type 1 error increases.
C)the probability of retaining the null hypothesis increases.
D )the probability of rejecting the null hypothesis decreases.

Question 7

The standard error of the difference between means:

A)cannot be properly estimated.
B)requires only one sample's characteristics.
C)is an estimate of the standard deviation in a sampling distribution of differences.
D)does not include the sample sizes.

Question 8

Accepting the null hypothesis for the means of two independent groups indicates that there is no statistically significant difference.

Question 9

When we retain the null hypothesis, we:

A)claim that a significant difference exists between groups.
B)have obtained a t-value greater than our critical t-value.
C)have committed a Type 1 error.
D)conclude that sampling error is responsible for our obtained difference.

Question 10

The symbols for a Type 1 error and Type 2 error are respectively

A)π, Ω
B)Ω, π
C)α, β
D)Β, α

Question 11

The null hypothesis in a two-tailed, independent t-test of means would be:

A)
B)
C)
D)

Question 12

The question below refers to the following situation:
A researcher is interested in the relationship between political party affiliation (Democrat Or Republican) and support for a woman's right to choose (Pro-Choice). In order to do this She uses a standardized measure for determining support for Pro-Choice. The higher the Person scores on the measure, the greater is his or her support for Pro-Choice.
If the researcher fails to find a significant difference, when in fact one exists in the Population:

A)a Type 1 error has been made.
B)a Type 2 error has been made.
C)the null hypothesis was correctly rejected.
D)the research hypothesis was correctly accepted.

Question 13

The larger the value of our obtained t:

A)the more probable that our results are due to chance alone.
B)the less probable that our results are due to chance alone.
C)the larger our critical t-value.
D )the larger the probability of making a Type 1 error.

Question 14

When we test hypotheses of differences between means, we:

A)compare our results to that of a probability distribution.
B)test to see if our obtained difference could have happened by chance.
C)calculate a type of z-score to locate our difference on a probability distribution.
D)All of the above are correct.

Question 15

With respect to α (alpha), which of the following statements is true?

A)As α increases, β (beta) increases.
B)α and β are unrelated.
C)Alpha is the level of probability at which the null hypothesis can be rejected with Confidence.
D)Alpha is the level of probability at which the null hypothesis can be retained with confidence.

Question 16

If we reject the null hypothesis when in reality the null hypothesis is true, we have:

A)made the correct decision.
B)made a Type 1 error.
C)made a Type 2 error.
D)none of the above

Question 17

When we risk committing a Type 1 error:

A)we risk rejecting the null hypothesis when it is true.
B)our sample size was too large.
C)we risk accepting the null hypothesis when it is false.
D)The cost of a Type 2 error is always greater.

Question 18

Which statement is true of α (alpha)?

A)Conventionally, social researchers set α = .05.
B)Alpha increases as our sample size decreases.
C)Stringent levels of α can provide absolute certainty.
D )All of the above are true.

Question 19

Which of the following does NOT exemplify a research hypothesis:

A)Southern states are more socially conservative than northern states.
B)Men are less monogamous than women.
C)Drivers of SUVs have the same personality type as drivers of pickup trucks.
D)High school graduates are more conservative than college graduates.

Question 20

The sampling distribution of differences between means approximates a normal curve
Whose __________ is zero.

A)mode
B)median
C)mean
D)st andard deviation

Question 21

Testing the difference between means or proportions requires random sampling.

Question 22

If the calculated t-value is smaller than the critical value of t we reject the null hypothesis.

Question 23

05 level of significance corresponds with a confidence interval of __________%.

Question 24

The question below refers to the following data:
A social researcher wants to test the hypothesis that college students who drink alcohol while text messaging create a different number of keystrokes than those who do not drink while they text. The social researcher studies 50 drinking texters and 50 non-drinking texters. The average number of keystrokes for the drinking texters was 142 with a standard deviation of 7.45. The average number of keystrokes for the non-drinking texters was 134
with a standard deviation of 6.81.
What is the research hypothesis? (Pay attention to the scenario.)

Question 25

The t-distribution more closely approximates the distribution of the normal curve when the degrees of freedom __________.

Question 26

The question below refers to the following data:
A social researcher wants to test the hypothesis that college students who drink alcohol while text messaging create a different number of keystrokes than those who do not drink while they text. The social researcher studies 50 drinking texters and 50 non-drinking texters. The average number of keystrokes for the drinking texters was 142 with a standard deviation of 7.45. The average number of keystrokes for the non-drinking texters was 134
with a standard deviation of 6.81.
Calculate t.

Question 27

The question below refers to the following data:
Dr. Chung, a renowned dietician, has consistently proclaimed the benefits of a balanced breakfast. To substantiate his claim, he asks participants to go without breakfast for one week. The following week he asks the same participants to make sure they eat a complete breakfast. Following each week, Dr. Chung asks each participant to rate their productivity for that week.
What is the null hypothesis in the example above?

Question 28

We predetermine our level of _____ for a hypothesis test on the basis of which type of error is more costly.

Question 29

English proficiency scores have been collected from 46 students before and after completing an English as a Second Language course. The degrees of freedom for our t-test are __________.

Question 30

The t-test can be used for testing the same sample measured twice as well as for two independent samples.

Question 31

If we surveyed random samples of 35 supervisors and 65 employees on a scale of job satisfaction, our degrees of freedom are: __________.

Question 32

If our obtained t-value is greater than our critical t-value, we believe that the null hypothesis is __________.

Question 33

The question below refers to the following:
The administration at a university is interested in studying if any relationship exists between satisfaction at the school and whether the student is a freshman or a senior. The school randomly surveys 10 freshmen and 10 seniors and asks them to rate how satisfied they are at the school on a scale of 1-10, where 10 is extremely satisfied and 1 is extremely dissatisfied. Here is the collected data:
What is the research hypothesis ?

Question 34

The question below refers to the following:
The administration at a university is interested in studying if any relationship exists between satisfaction at the school and whether the student is a freshman or a senior. The school randomly surveys 10 freshmen and 10 seniors and asks them to rate how satisfied they are at the school on a scale of 1-10, where 10 is extremely satisfied and 1 is extremely dissatisfied. Here is the collected data:
What are your conclusions about the null hypothesis?

Question 35

The question below refers to the following:
The administration at a university is interested in studying if any relationship exists between satisfaction at the school and whether the student is a freshman or a senior. The school randomly surveys 10 freshmen and 10 seniors and asks them to rate how satisfied they are at the school on a scale of 1-10, where 10 is extremely satisfied and 1 is extremely dissatisfied. Here is the collected data:
What are the degrees of freedom?

Question 36

The probabilities of a Type 1 error and a Type 2 error are __________ related.

Question 37

The question below refers to the following:
The administration at a university is interested in studying if any relationship exists between satisfaction at the school and whether the student is a freshman or a senior. The school randomly surveys 10 freshmen and 10 seniors and asks them to rate how satisfied they are at the school on a scale of 1-10, where 10 is extremely satisfied and 1 is extremely dissatisfied. Here is the collected data:
What is the null hypothesis?

Question 38

The question below refers to the following:
The administration at a university is interested in studying if any relationship exists between satisfaction at the school and whether the student is a freshman or a senior. The school randomly surveys 10 freshmen and 10 seniors and asks them to rate how satisfied they are at the school on a scale of 1-10, where 10 is extremely satisfied and 1 is extremely dissatisfied. Here is the collected data:
Are the results significant? Why or why not?

Question 39

The question below refers to the following:
The administration at a university is interested in studying if any relationship exists between satisfaction at the school and whether the student is a freshman or a senior. The school randomly surveys 10 freshmen and 10 seniors and asks them to rate how satisfied they are at the school on a scale of 1-10, where 10 is extremely satisfied and 1 is extremely dissatisfied. Here is the collected data:
Calculate t.

Question 40

The question below refers to the following data:
A social researcher wants to test the hypothesis that college students who drink alcohol while text messaging create a different number of keystrokes than those who do not drink while they text. The social researcher studies 50 drinking texters and 50 non-drinking texters. The average number of keystrokes for the drinking texters was 142 with a standard deviation of 7.45. The average number of keystrokes for the non-drinking texters was 134 with a standard deviation of 6.81.
What is the null hypothesis? (Pay attention to the scenario.)

Question 41

Democrats and Republicans were surveyed on their support of healthcare reform using a standardized measure (high scores representing greater support of healthcare reform).
Using the data provided, calculate t.

Question 42

The question below refers to the following data:
A social researcher wants to test the hypothesis that college students who drink alcohol while text messaging create a different number of keystrokes than those who do not drink while they text. The social researcher studies 50 drinking texters and 50 non-drinking texters. The average number of keystrokes for the drinking texters was 142 with a standard deviation of 7.45. The average number of keystrokes for the non-drinking texters was 134 with a standard deviation of 6.81.
What are your conclusions about the null hypothesis?

Question 43

The question below refers to the following situation:
A sample of low-income and high-income individuals was surveyed concerning their opinions on television violence. Those who responded that television violence has become excessive are shown below.
Calculate the combined sample proportion.

Question 44

The question below refers to the following situation:
A sample of low-income and high-income individuals was surveyed concerning their opinions on television violence. Those who responded that television violence has become excessive are shown below.
What is the standard error of the difference?

Question 45

The question below refers to the following situation:
A sample of low-income and high-income individuals was surveyed concerning their opinions on television violence. Those who responded that television violence has become excessive are shown below.
Calculate the proportion of low-income and high-income people who believe excessive violence is shown on television.

Question 46

Some researchers contend that anxiety is detrimental to performance, while other researchers contend that anxiety actually enhances performance. To help shed light on this question, Dr. Patterson has her participants work on crossword puzzles both before and after being exposed to an anxiety-inducing stimulus. The scores on an anxiety rating scale from her 4 participants are presented below.
Using α = .05, test the null hypothesis that the two groups do not differ.

Question 47

The question below refers to the following data:
A social researcher wants to test the hypothesis that college students who drink alcohol while text messaging create a different number of keystrokes than those who do not drink while they text. The social researcher studies 50 drinking texters and 50 non-drinking texters. The average number of keystrokes for the drinking texters was 142 with a standard deviation of 7.45. The average number of keystrokes for the non-drinking texters
was 134 with a standard deviation of 6.81.
What are your degrees of freedom?

Question 48

The question below refers to the following situation:
A sample of low-income and high-income individuals was surveyed concerning their opinions on television violence. Those who responded that television violence has become excessive are shown below.
Translate the difference between proportions into units of the standard error of the difference (standard z-value).

Question 49

The question below refers to the following data:
A social researcher wants to test the hypothesis that college students who drink alcohol while text messaging create a different number of keystrokes than those who do not drink while they text. The social researcher studies 50 drinking texters and 50 non-drinking texters. The average number of keystrokes for the drinking texters was 142 with a standard deviation of 7.45. The average number of keystrokes for the non-drinking texters
was 134 with a standard deviation of 6.81.
Are your results significant, and if so, at what level?