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In your own words, what is a P-value?

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A P-value is the probability o...

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Children as young as 2 years of age, upon seeing an object placed under a pillow in a familiar setting at home, will understand to look for it after an interval of time and be able to find it. Investigators believe this capability will be less pronounced in a laboratory situation, where the child is away from the familiar setting of home. Let p denote the proportion of 2-year-olds than have this understanding in the home situation, and suppose that p = 0.35. The investigators wish to determine whether the proportion that remembers is less when the child is away from home. a)What is the appropriate null hypothesis? b)What is the appropriate alternative hypothesis? c)In your own words, distinguish between a Type I and a Type II error in this context.

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a)H0 : p = 0.35
b)Ha : p < 0.35
c)A Type I...

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In a test of H0: p = 0.45 versus Ha: p < 0.45, the value of the z test statistic was calculated to be z = In a test of H<sub>0</sub>: p = 0.45 versus H<sub>a</sub>: p < 0.45, the value of the z test statistic was calculated to be z = . Which of the following is the P-value for this test? ​ A) 0.1230 B) 0.2360 C) 0.2500 D) 0.2912 E) 0.3020 . Which of the following is the P-value for this test? ​


A) 0.1230
B) 0.2360
C) 0.2500
D) 0.2912
E) 0.3020

F) A) and E)
G) None of the above

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Researchers conducted a survey in which each person in a representative sample of 2135 developers had been asked about the main priorities when choosing a new job. When asked about a remote work opportunity, 1238of the developers in the sample said that this is one of the main priorities in the search for work. These data were used to test Researchers conducted a survey in which each person in a representative sample of 2135 developers had been asked about the main priorities when choosing a new job. When asked about a remote work opportunity, 1238of the developers in the sample said that this is one of the main priorities in the search for work. These data were used to test versus and the null hypothesis was rejected. Is it reasonable to say that the data provide strong support for the alternative hypothesis? Is it reasonable to say that the data provide strong evidence against the null hypothesis? A) The data do not provide strong support for the alternative hypothesis and provide strong evidence against the null hypothesis. B) The data provide strong support for the alternative hypothesis and provide strong evidence against the null hypothesis. C) The data provide strong support for the alternative hypothesis and do not provide strong evidence against the null hypothesis. D) The data do not provide strong support for the alternative hypothesis and do not provide strong evidence against the null hypothesis. versus Researchers conducted a survey in which each person in a representative sample of 2135 developers had been asked about the main priorities when choosing a new job. When asked about a remote work opportunity, 1238of the developers in the sample said that this is one of the main priorities in the search for work. These data were used to test versus and the null hypothesis was rejected. Is it reasonable to say that the data provide strong support for the alternative hypothesis? Is it reasonable to say that the data provide strong evidence against the null hypothesis? A) The data do not provide strong support for the alternative hypothesis and provide strong evidence against the null hypothesis. B) The data provide strong support for the alternative hypothesis and provide strong evidence against the null hypothesis. C) The data provide strong support for the alternative hypothesis and do not provide strong evidence against the null hypothesis. D) The data do not provide strong support for the alternative hypothesis and do not provide strong evidence against the null hypothesis. and the null hypothesis was rejected. Is it reasonable to say that the data provide strong support for the alternative hypothesis? Is it reasonable to say that the data provide strong evidence against the null hypothesis?


A) The data do not provide strong support for the alternative hypothesis and provide strong evidence against the null hypothesis.
B) The data provide strong support for the alternative hypothesis and provide strong evidence against the null hypothesis.
C) The data provide strong support for the alternative hypothesis and do not provide strong evidence against the null hypothesis.
D) The data do not provide strong support for the alternative hypothesis and do not provide strong evidence against the null hypothesis.

E) B) and C)
F) A) and D)

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B

The article reports that in a random sample of 1760 residents of the city, 597 answered "yes" to the following question: "Are you satisfied with the ecological situation in your city?" The authors were interested in using these data to determine if there is convincing evidence that less than 40% residents of the city are satisfied with the ecological situation in the city. Answer the following four key questions and indicate whether the method that you would consider would be a large-sample hypothesis test for a population proportion. The article reports that in a random sample of 1760 residents of the city, 597 answered yes to the following question: Are you satisfied with the ecological situation in your city? The authors were interested in using these data to determine if there is convincing evidence that less than 40% residents of the city are satisfied with the ecological situation in the city. Answer the following four key questions and indicate whether the method that you would consider would be a large-sample hypothesis test for a population proportion. ​ A) Hypothesis testing, sample data, one categorical variable, one sample.A large-sample hypothesis test for a population proportion would not be appropriate. B) Estimation, sample data, one numerical variable, one sample.A large-sample hypothesis test for a population proportion would be appropriate. C) Hypothesis testing, sample data, one numerical variable, one sample.A large-sample hypothesis test for a population proportion would not be appropriate. D) Estimation, sample data, two categorical variables, one sample.A large-sample hypothesis test for a population proportion would be appropriate. E) Hypothesis testing, sample data, one categorical variable, one sample.A large-sample hypothesis test for a population proportion would be appropriate. ​


A) Hypothesis testing, sample data, one categorical variable, one sample.A large-sample hypothesis test for a population proportion would not be appropriate.
B) Estimation, sample data, one numerical variable, one sample.A large-sample hypothesis test for a population proportion would be appropriate.
C) Hypothesis testing, sample data, one numerical variable, one sample.A large-sample hypothesis test for a population proportion would not be appropriate.
D) Estimation, sample data, two categorical variables, one sample.A large-sample hypothesis test for a population proportion would be appropriate.
E) Hypothesis testing, sample data, one categorical variable, one sample.A large-sample hypothesis test for a population proportion would be appropriate.

F) A) and D)
G) A) and E)

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Assuming a random sample from a large population, for which of the following null hypotheses and sample sizes is the large-sample z test appropriate? ​


A) Assuming a random sample from a large population, for which of the following null hypotheses and sample sizes is the large-sample z test appropriate? ​ A) B) C) D) E)
B) Assuming a random sample from a large population, for which of the following null hypotheses and sample sizes is the large-sample z test appropriate? ​ A) B) C) D) E)
C) Assuming a random sample from a large population, for which of the following null hypotheses and sample sizes is the large-sample z test appropriate? ​ A) B) C) D) E)
D) Assuming a random sample from a large population, for which of the following null hypotheses and sample sizes is the large-sample z test appropriate? ​ A) B) C) D) E)
E) Assuming a random sample from a large population, for which of the following null hypotheses and sample sizes is the large-sample z test appropriate? ​ A) B) C) D) E)

F) A) and E)
G) B) and E)

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E

One of the early decisions that must be made when performing a hypothesis test is the choice of significance level. Briefly describe the considerations that go into making this decision.

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To decide on the significance level, the...

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The average household income for Florida residents was $49,852 in 2015. You are interested in determining if there is evidence that the mean household income in the current year is greater than the known average from 2015. Answer the following four key questions and indicate whether the method that you would consider would be a large-sample hypothesis test for a population proportion. The average household income for Florida residents was $49,852 in 2015. You are interested in determining if there is evidence that the mean household income in the current year is greater than the known average from 2015. Answer the following four key questions and indicate whether the method that you would consider would be a large-sample hypothesis test for a population proportion. ​ A) Estimation, sample data, one numerical variable, one sample.A large-sample hypothesis test for a population proportion would be appropriate. B) Hypothesis testing, sample data, one categorical variable, one sample.A large-sample hypothesis test for a population proportion would be appropriate. C) Hypothesis testing, sample data, one numerical variable, one sample.A large-sample hypothesis test for a population proportion would not be appropriate. D) Hypothesis testing, sample data, two numerical variables, one sample.A large-sample hypothesis test for a population proportion would not be appropriate. E) Estimation, sample data, one categorical variable, one sample.A large-sample hypothesis test for a population proportion would not be appropriate. ​


A) Estimation, sample data, one numerical variable, one sample.A large-sample hypothesis test for a population proportion would be appropriate.
B) Hypothesis testing, sample data, one categorical variable, one sample.A large-sample hypothesis test for a population proportion would be appropriate.
C) Hypothesis testing, sample data, one numerical variable, one sample.A large-sample hypothesis test for a population proportion would not be appropriate.
D) Hypothesis testing, sample data, two numerical variables, one sample.A large-sample hypothesis test for a population proportion would not be appropriate.
E) Estimation, sample data, one categorical variable, one sample.A large-sample hypothesis test for a population proportion would not be appropriate.

F) A) and D)
G) B) and D)

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It is customary to say that the result of a hypothesis test is statistically significant when the P-value is smaller than α.

A) True
B) False

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You are interested in determining whether there is strong evidence in support of the claim that less than 40% of retired adults have a part-time job. To answer this question, what null and alternative hypotheses should you test? ​


A) H0: p = 0.4 versus Ha: p > 0.4
B) H0: p = 0.4 versus Ha: p < 0.4
C) H0: p = 0.4 versus Ha: p ≠ 0.4
D) H0: p < 0.4 versus Ha: p > 0.4
E) H0: p < 0.4 versus Ha: p = 0.4

F) D) and E)
G) B) and E)

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A type II error is made by failing to reject a false null hypothesis.

A) True
B) False

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Assuming the same sample size is used, how does changing the significance level from 0.2 to 0.05 affect the power of a test? ​


A) The power decreases.
B) The power increases.
C) The power does not change.
D) The power does change, but it might either decrease or increase.
E) It is not possible to predict whether the power will increase, decrease, or remain the unchanged.

F) A) and B)
G) None of the above

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Small P-values indicate that the observed sample is inconsistent with the null hypothesis.

A) True
B) False

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Explain in your own words what a hypothesis test is.

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In a hypothesis test, we are u...

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β is called the observed significance level.

A) True
B) False

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All other things being equal, choosing a smaller value of α will increase the probability of making a type II error.

A) True
B) False

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Define, using your own words, a test statistic.

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A test statistic is ...

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Assuming the same significance level is used, how does increasing the sample size from 50 to 100 affect the power of a test? ​


A) The power decreases.
B) The power increases.
C) The power does not change.
D) The power does change, but it might either decrease or increase.
E) It is not possible to predict whether the power will increase, decrease, or remain the unchanged.

F) B) and C)
G) B) and E)

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If the null hypothesis is not rejected, there is strong statistical evidence that the null hypothesis is true.

A) True
B) False

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False

Describe the two types of errors that might be made when a hypothesis test is carried out. ​


A) A Type I error is rejecting Ho when Ho is true.A Type II error is failing to reject Ho when Ho is false.
B) A Type I error is rejecting Ho when Ho is false.A Type II error is failing to reject Ho when Ho is true.
C) A Type I error is failing to reject Ho when Ho is true.A Type II error is rejecting Ho when Ho is true.
D) A Type I error is rejecting Ho when Ho is true.A Type II error is failing to reject Ho when Ho is true.
E) A Type I error is rejecting Ho when Ho is false.A Type II error is failing to reject Ho when Ho is false.

F) C) and D)
G) A) and B)

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