Type I Error And Type II Error – Null Hypothesis – Statistics

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Type I Error, Type II Error, Hypothesis Test, Null Hypothesis, Population Mean

The key terms in these Statistic chapters include Descriptive Technique, Hypothesis Test, Sample, Type I Error, Population, The Probability, Type II Error, Null Hypothesis, Sample Mean, Reject The Null Hypothesis, Treatment Effect, Inferential Technique, Population Mean, Frequency Distribution, Critical Region.


Which of the following accurately describes a hypothesis test?

a) a descriptive technique that allows researchers to describe a sample
b) a descriptive technique that allows researchers to describe a population
c) an inferential technique that uses the data from a sample to draw inferences about a population
d) an inferential technique that uses information about a population to make predictions about a sample


A hypothesis test involves a comparison of which two elements?

a) research results from a sample and a hypothesis about a population
b) research results from a population and a hypothesis about a sample
c) research results from a population and a hypothesis about the population
d) research results from a sample and a hypothesis about the sample


For a hypothesis test evaluating the effect of a treatment on a population mean, what basic assumption is made concerning the treatment effect?

a) if there is a treatment effect, it will increase the scores
b) if there is a treatment effect, it will decrease the scores
c) if there is a treatment effect, it will add (or subtract) a constant to each score
d) if there is a treatment effect, it will multiply (or divide) each score by a constant


In general, the null hypothesis states that the treatment has no effect on the population mean.

True

Which of the following is directly addressed by the null hypothesis?

a) the population before treatment
b) the population after treatment
c) the sample before treatment
d) the sample after treatment


A researcher selects a sample and administers a treatment to the individuals in the sample. If the sample is used for a hypothesis test, what does the null hypothesis (Ho) say about the treatment?

a) the treatment causes a change in the scores
b) the treatment adds a constant to each score
c) the treatment multiplies each score by a constant
d) the treatment has no effect on the scores


A researcher selects a sample and administers a treatment to the individuals in the sample. If the sample is used for a hypothesis test, what does the alternate hypothesis (H1) say about the treatment?

a) the treatment causes a change in the scores
b) the treatment adds a constant to each score
c) the treatment multiplies each score by a constant
d) the treatment has no effect on the scores


Which of the following accurately describes the critical region?

a) outcomes with a very low probability if the null hypothesis is true
b) outcomes with a high probability if the null hypothesis is true
c) outcomes with a very low probability whether or not the null hypothesis is true
d) outcomes with a high probability whether or not the null hypothesis is true


The null hypothesis predicts a specific value for the population mean.

True

With a = .05, how are the boundaries for the critical region determined?

a) boundaries are drawn so there is 2.5% (.025) in each tail of the distribution
b) boundaries are drawn so there is 5% (.05) in each tail of the distribution
c) boundaries are drawn so there is 10% (.10) in each tail of the distribution
d) boundaries are drawn so there is 5% (.05) in the center of the distribution


Which of the following accurately describes a hypothesis test?

a) a descriptive technique that allows researchers to describe a sample
b) a descriptive technique that allows researchers to describe a population
c) an inferential technique that uses the data from a sample to draw inferences about a population
d) an inferential technique that uses information about a population to make predictions about a sample


A hypothesis test involves a comparison of which two elements?

a) research results from a sample and a hypothesis about a population
b) research results from a population and a hypothesis about a sample
c) research results from a population and a hypothesis about the population
d) research results from a sample and a hypothesis about the sample


For a hypothesis test evaluating the effect of a treatment on a population mean, what basic assumption is made concerning the treatment effect?

a) if there is a treatment effect, it will increase the scores
b) if there is a treatment effect, it will decrease the scores
c) if there is a treatment effect, it will add (or subtract) a constant to each score
d) if there is a treatment effect, it will multiply (or divide) each score by a constant


The null hypothesis states that the sample mean (after treatment) is equal to the original population mean (before treatment).

False

Which of the following is directly addressed by the null hypothesis?

a) the population before treatment
b) the population after treatment
c) the sample before treatment
d) the sample after treatment


If a hypothesis test produces a z-score in the critical region, what decision should be made?

a) reject the alternative hypothesis
b) fail to reject the alternative hypothesis
c) reject the null hypothesis
d) fail to reject the null hypothesis


If a treatment has a very small effect, what is a likely outcome for a hypothesis test evaluating the treatment?

a) a type I error
b) a type II error
c) correctly reject the null hypothesis
d) correctly fail to reject the null hypothesis


You complete a hypothesis test using a = .05, and based on the evidence from the sample, your decision is to reject the null hypothesis. Which of the following is true?

a) you have made a type I error
b) you have made a type II error
c) you might have made a type I error, but the probability is less than 5%
d) you have made the correct decision


You complete a hypothesis test using a = .05, and based on the evidence from the sample, your decision is to reject the null hypothesis. If the treatment actually does have an effect, which of the following is true?

a) you have made a type I error
b) you have made a type II error
c) you might have made a type I error, but the probability is only 5% at most
d) you have made the correct decision


The null hypothesis predicts a specific value for the population mean.

True

In general, the null hypothesis states that the treatment has no effect on the population mean.

True


The null hypothesis states that the sample mean (after treatment) is equal to the original population mean (before treatment).

False


In most situations, researchers would like the hypothesis test to reject the null hypothesis.

True


The critical region for a hypothesis test consists of sample outcomes that are very unlikely to occur if the null hypothesis is true.

True


If a hypothesis test leads to rejecting the null hypothesis, it means that the sample data failed to provide sufficient evidence to conclude that the treatment has an effect.

False


If the sample data are in the critical region with a = .05, then the same sample data would still be in the critical region if a were changed to .01.

False


If the sample data are in the critical region with a = .01, then the same sample data would still be in the critical region if a were changed to .05.

True

A sample of n = 25 individuals is selected from a population with u = 80, and a treatment is administered to the sample. What is the expected if the treatment has no effect?

a) the sample mean should be very different from 80 and should lead you to reject the null hypothesis
b) the sample mean should be very different from 80 and should lead you to fail to reject the null hypothesis
c) the sample mean should be close to 80 and should lead you to reject the null hypothesis
d) the sample mean should be close 80 and should lead you to fail to reject the null hypothesis


Which of the following is an accurate definition of a Type I error?

a) rejecting a false null hypothesis
b) rejecting a true null hypothesis
c) failing to reject a false null hypothesis
d) failing to reject a true null hypothesis


Which of the following is an accurate definition of a Type II error?

a) rejecting a false null hypothesis
b) rejecting a true null hypothesis
c) failing to reject a false null hypothesis
d) failing to reject a true null hypothesis


A frequency distribution graph represents frequencies associated with scores for a variable with vertical bars that have space between them. Which scale of measurement was used to measure this variable?

Nominal

What is the consequence of a Type I error?

a) concluding that a treatment has an effect when it really does
b) concluding that a treatment has no effect when it really has no effect
c) concluding that a treatment has no effect when it really does
d) concluding that a treatment has an effect when it really has no effect


What is the consequence of a Type II error?

a) concluding that a treatment has an effect when it really does
b) concluding that a treatment has no effect when it really has no effect
c) concluding that a treatment has no effect when it really does
d) concluding that a treatment has an effect when it really has no effect


Which of the following statements must be false regarding a distribution of scores?

No individual has a score exactly equal to the mode.

When is there a risk of a Type I error?

a) whenever Ho is rejected
b) whenever H1 is rejected
c) whenever the decision is “fail to reject Ho”
d) the risk of a Type I error is independent of the decision from a hypothesis test


When is there a risk of a Type II error?

a) whenever Ho is rejected
b) whenever H1 is rejected
c) whenever the decision is “fail to reject Ho”
d) the risk of a Type II error is independent of the decision from a hypothesis test


If a treatment has a very small effect, what is a likely outcome for a hypothesis test evaluating the treatment?

a) a type I error
b) a type II error
c) correctly reject the null hypothesis
d) correctly fail to reject the null hypothesis


You complete a hypothesis test using a = .05, and based on the evidence from the sample, your decision is to reject the null hypothesis. Which of the following is true?

a) you have made a type I error
b) you have made a type II error
c) you might have made a type I error, but the probability is less than 5%
d) you have made the correct decision


You complete a hypothesis test using a = .05, and based on the evidence from the sample, your decision is to reject the null hypothesis. If the treatment actually does have an effect, which of the following is true?

a) you have made a type I error
b) you have made a type II error
c) you might have made a type I error, but the probability is only 5% at most
d) you have made the correct decision


In most situations, researchers would like the hypothesis test to reject the null hypothesis.

True

The critical region for a hypothesis test consists of sample outcomes that are very unlikely to occur if the null hypothesis is true.

True


If a hypothesis test leads to rejecting the null hypothesis, it means that the sample data failed to provide sufficient evidence to conclude that the treatment has an effect.

False


If the sample data are in the critical region with a = .05, then the same sample data would still be in the critical region if a were changed to .01.

False


If the sample data are in the critical region with a = .01, then the same sample data would still be in the critical region if a were changed to .05.

True


Which of the following statements must be false regarding a distribution of scores?

No individual has a score exactly equal to the mode.


One sample with n = 4 scores has a mean of M = 12, and a second sample with n = 6 scores has a mean of M = 8. If the two samples are combined, what is the mean for the combined set of scores?

M = 9.6

A frequency distribution graph represents frequencies associated with scores for a variable with vertical bars that have space between them. Which scale of measurement was used to measure this variable?

Nominal


A researcher surveys a sample of n = 20 college students and asks each person to identify their favorite movie. If the data were organized in a frequency distribution table, what would be included in the last column?

List of frequencies


For the scores in the following table, what is the value of ΣX 2? (X: 3,2,1 f: 1, 2, 4)

21


A set of scores ranges from a high of X = 45 to a low of X = 11. If these scores were placed in an appropriately designed grouped frequency distribution table, which of the following would be the bottom interval in the table?

10-14


Which statement below must be false regarding a distribution of scores?

75% of the scores are above the median


Which statement below is consistent with computing a weighted average of two individual samples?

A computed weighted average will always be closer to the mean average of the larger sample than the mean average of the smaller sample.


One item on a questionnaire asks students how many times per day in a typical week they make a call on their cell phones. The responses for a sample of n = 12 students are summarized in the frequency distribution. What is the best measure of central tendency for these data?

X f

5+ 5

4 4

3 1

2 0

1 2

0 0

The median


Which statement below is correct regarding a grouped frequency distribution table?

The ∑x cannot be determined.


Which term is used to describe the shape of a frequency distribution graph in which most scores pile up on the left-hand side of the graph and taper off to the right?

Positively skewed


Which of the following accurately describes the critical region?

a) outcomes with a very low probability if the null hypothesis is true
b) outcomes with a high probability if the null hypothesis is true
c) outcomes with a very low probability whether or not the null hypothesis is true
d) outcomes with a high probability whether or not the null hypothesis is true


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