Exam 10: Asking and Answering Questions About a Population Proportion

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?

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(Multiple Choice)

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Question 1

Correct Answer:

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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?

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(Multiple Choice)

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Question 2

Correct Answer:

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

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(True/False)

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Question 3

Correct Answer:

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False

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

(Multiple Choice)

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Question 4

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

(Essay)

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Question 5

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?

(Multiple Choice)

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Question 6

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.

(Multiple Choice)

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Question 7

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

(True/False)

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Question 8

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

(True/False)

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Question 9

β is called the observed significance level.

(True/False)

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Question 10

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

(Multiple Choice)

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Question 11

Define, using your own words, a test statistic.

(Essay)

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Question 12

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?

(Multiple Choice)

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Question 13

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.

(Essay)

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Question 14

In a test of H₀: p = 0.45 versus H_a: 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?

(Multiple Choice)

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Question 15

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

(True/False)

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Question 16

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.

(Essay)

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Question 17

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

(True/False)

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Question 18

Explain in your own words what a hypothesis test is.

(Essay)

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Question 19

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.

(Multiple Choice)

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Question 20

Showing 1 - 20 of 31

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?

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

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

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

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?

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

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

β is called the observed significance level.

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

Define, using your own words, a test statistic.

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?

In a test of H₀: p = 0.45 versus H_a: 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 type II error is made by failing to reject a false null hypothesis.

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.

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

Explain in your own words what a hypothesis test is.

Collecting Data in Reasonable Ways

Graphical Methods for Describing Data Distributions

Numerical Methods for Describing Data Distributions

Describing Bivariate Numerical Data

Probability

Random Variables and Probability Distributions

An Overview of Statistical Inference - Learning From Data

Sampling Variability and Sampling Distributions

Estimating a Population Proportion

Asking and Answering Questions About the Difference Between Two Proportions

Asking and Answering Questions About a Population Mean

Asking and Answering Questions About the Difference Between Two Means

Learning From Categorical Data

Understanding Relationships - Numerical Data Part 2

Asking and Answering Questions About More Than Two Means

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Exam 10: Asking and Answering Questions About a Population Proportion

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? ​

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

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

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

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? ​

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

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

β is called the observed significance level.

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

Define, using your own words, a test statistic.

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? ​

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 = . Which of the following is the P-value for this test? ​

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

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.

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

Explain in your own words what a hypothesis test is.

Collecting Data in Reasonable Ways

Graphical Methods for Describing Data Distributions

Numerical Methods for Describing Data Distributions

Describing Bivariate Numerical Data

Probability

Random Variables and Probability Distributions

An Overview of Statistical Inference - Learning From Data

Sampling Variability and Sampling Distributions

Estimating a Population Proportion

Asking and Answering Questions About the Difference Between Two Proportions

Asking and Answering Questions About a Population Mean

Asking and Answering Questions About the Difference Between Two Means

Learning From Categorical Data

Understanding Relationships - Numerical Data Part 2

Asking and Answering Questions About More Than Two Means

Filters

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?

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

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?

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

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?

In a test of H₀: p = 0.45 versus H_a: 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?