Students of two sections of a history course took a common final examination. The course instructor examines the variance in scores between the two sections. He selects random samples of n1 = 11 and n2 = 16 with sample variances of and = 200, respectively. Assuming that the population distributions are normal, construct a 90% confidence interval for the ratio of the population variance.

A) [0.90, 2.41] B) [0.50, 2.00] C) [0.25, 4.00] D) [0.79, 5.70] A) [0.90, 2.41] B) [0.50, 2.00] C) [0.25, 4.00] D) [0.79, 5.70]

Which of the following is the formula for the sample variance s2 when used as an estimate of σ2 for a random sample of n observations from a population?

A) s2 = B) s2 = C) s2 = D) s2 = A) s2 = B) s2 = C) s2 = D) s2 =

The following are the competing hypotheses and the relevant summary statistics Η0: / ≤ 1, ΗA: / > 1. Which of the following statements is correct, regarding the assumptions for conducting the hypothesis test?

A) The samples are drawn from populations that are not normally distributed. B) The values in one group are related to the values in the other group. C) The difference of the sample variances is used to test the hypotheses. D) The samples are independent and drawn from normally distributed populations. A) The samples are drawn from populations that are not normally distributed. B) The values in one group are related to the values in the other group. C) The difference of the sample variances is used to test the hypotheses. D) The samples are independent and drawn from normally distributed populations.

Exam 11: Statistical Inference Concerning Variance

The formula for the confidence interval of the population variance σ² is valid only when the random sample is drawn from a ________ distributed population.

(Short Answer)

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Question 41

Inference for two population variances is done through their difference - .

(True/False)

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Question 42

Students of two sections of a history course took a common final examination. The course instructor examines the variance in scores between the two sections. He selects random samples of n₁ = 11 and n₂ = 16 with sample variances of and = 200, respectively. Assuming that the population distributions are normal, construct a 90% confidence interval for the ratio of the population variance.

(Multiple Choice)

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Question 43

Becky owns a diner and is concerned about sustaining the business. She wants to ascertain if the standard deviation of the profits for each week is greater than $250. The details of the profits for the week are (in dollars) 1,743 1,438 1,212 1,705 1,985 1,857 1,916 Assume that profits are normally distributed. Which of the following is the correct value of the test statistic?

(Multiple Choice)

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Question 44

The population variance is one of the most widely used quantitative measures of risk in investments.

(True/False)

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Question 45

Which of the following is the formula for the sample variance s² when used as an estimate of σ² for a random sample of n observations from a population?

(Multiple Choice)

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Question 46

If P( ≥ x) = 0.05, then the value of x is

(Multiple Choice)

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Question 47

The following table shows the heights (in inches) of individuals recorded recently for two families, the Williamses and the Thomases, in Chicago, Illinois: a. Construct a 95% interval estimate of the ratio of the population variances. B) Using the computed confidence interval, test if the ratio of the population variances differs from one at the 5% significance level. Explain.

(Essay)

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Question 48

Statistical inference for σ² is based on the F distribution.

(True/False)

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Question 49

(Use Excel) The following are the prices (in $1,000s) of 20 houses sold recently in Vancouver, Washington. A real estate agent believes that the standard deviation of house prices is less than 70 units, where each unit equals $1,000. Assume house prices are normally distributed. a. State the null and the alternative hypotheses for the test. B) Calculate the value of the test statistic. C) Use Excel's function (either CHISQ.DIST.RT or CHISQ.DIST) to calculate the p-value. D) At α = 0.10, what is the conclusion? Is the agent's claim supported by the data?

(Essay)

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Question 50

The formula for constructing the confidence interval for the ratio of two population variances is based on the assumption that the sample variances are computed from independently drawn samples from two non-normally distributed populations.

(True/False)

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Question 51

We can use Excel's function ________ that returns the right-tailed probability of the chi-square distribution.

(Short Answer)

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Question 52

A financial analyst maintains that the risk, measured by the variance, of investing in emerging markets is more than 280(%)². Data on 20 stocks from emerging markets revealed the following sample results: = 12.1% and s² = 361(%)². Assume that the returns are normally distributed. Which of the following is the correct conclusion of the financial analyst's claim?

(Multiple Choice)

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Question 53

Which of the following R functions is used to calculate the exact left-tail probability for a distribution?

(Multiple Choice)

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Question 54

Consider the hypotheses H₀: σ² = 169, H_A: σ² ≠ 169. A sample variance of 98 is obtained from a random sample of 10 observations drawn from a normally distributed population. At 1% significance level, conduct a test for the population variance using the p-value approach.

(Essay)

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Question 55

The following are the competing hypotheses and the relevant summary statistics Η₀: / ≤ 1, Η_A: / > 1. Which of the following statements is correct, regarding the assumptions for conducting the hypothesis test?

(Multiple Choice)

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Question 56

Which of the following is the value of for a 99% confidence level and degrees of freedom equal 6?

(Multiple Choice)

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Question 57

The values of the distribution range from negative infinity to infinity.

(True/False)

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Question 58

For a two-tailed test about two population variances, the null hypothesis is given by

(Multiple Choice)

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Question 59

A financial analyst maintains that the risk, measured by the variance, of investing in emerging markets is more than 280(%)². Data on 20 stocks from emerging markets revealed the following sample results: = 12.1% and s²= 361(%)². Assume that the returns are normally distributed. Which of the following are appropriate hypotheses to test the analyst's claim?

(Multiple Choice)

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Question 60

Showing 41 - 60 of 120

The formula for the confidence interval of the population variance σ² is valid only when the random sample is drawn from a ________ distributed population.

Inference for two population variances is done through their difference - .

The population variance is one of the most widely used quantitative measures of risk in investments.

Which of the following is the formula for the sample variance s² when used as an estimate of σ² for a random sample of n observations from a population?

If P( ≥ x) = 0.05, then the value of x is

Statistical inference for σ² is based on the F distribution.

The formula for constructing the confidence interval for the ratio of two population variances is based on the assumption that the sample variances are computed from independently drawn samples from two non-normally distributed populations.

We can use Excel's function ________ that returns the right-tailed probability of the chi-square distribution.

Which of the following R functions is used to calculate the exact left-tail probability for a distribution?

Consider the hypotheses H₀: σ² = 169, H_A: σ² ≠ 169. A sample variance of 98 is obtained from a random sample of 10 observations drawn from a normally distributed population. At 1% significance level, conduct a test for the population variance using the p-value approach.

The following are the competing hypotheses and the relevant summary statistics Η₀: / ≤ 1, Η_A: / > 1. Which of the following statements is correct, regarding the assumptions for conducting the hypothesis test?

Which of the following is the value of for a 99% confidence level and degrees of freedom equal 6?

The values of the distribution range from negative infinity to infinity.

For a two-tailed test about two population variances, the null hypothesis is given by

Statistics and Data

Tabular and Graphical Methods

Numerical Descriptive Measures

Introduction to Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Testing

Statistical Inference Concerning Two Populations

Chi-Square Tests

Analysis of Variance

Regression Analysis

Inference With Regression Models

Regression Models for Nonlinear Relationships

Regression Models With Dummy Variables

Time Series and Forecasting

Returns, Index Numbers, and Inflation

Nonparametric Tests

Filters

Exam 11: Statistical Inference Concerning Variance

The formula for the confidence interval of the population variance σ2 is valid only when the random sample is drawn from a ________ distributed population.

Inference for two population variances is done through their difference - .

The population variance is one of the most widely used quantitative measures of risk in investments.

Which of the following is the formula for the sample variance s2 when used as an estimate of σ2 for a random sample of n observations from a population?

If P( ≥ x) = 0.05, then the value of x is

Statistical inference for σ2 is based on the F distribution.

The formula for constructing the confidence interval for the ratio of two population variances is based on the assumption that the sample variances are computed from independently drawn samples from two non-normally distributed populations.

We can use Excel's function ________ that returns the right-tailed probability of the chi-square distribution.

Which of the following R functions is used to calculate the exact left-tail probability for a distribution?

Consider the hypotheses H0: σ2 = 169, HA: σ2 ≠ 169. A sample variance of 98 is obtained from a random sample of 10 observations drawn from a normally distributed population. At 1% significance level, conduct a test for the population variance using the p-value approach.

The following are the competing hypotheses and the relevant summary statistics Η0: / ≤ 1, ΗA: / > 1. Which of the following statements is correct, regarding the assumptions for conducting the hypothesis test?

Which of the following is the value of for a 99% confidence level and degrees of freedom equal 6?

The values of the distribution range from negative infinity to infinity.

For a two-tailed test about two population variances, the null hypothesis is given by

Statistics and Data

Tabular and Graphical Methods

Numerical Descriptive Measures

Introduction to Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Testing

Statistical Inference Concerning Two Populations

Chi-Square Tests

Analysis of Variance

Regression Analysis

Inference With Regression Models

Regression Models for Nonlinear Relationships

Regression Models With Dummy Variables

Time Series and Forecasting

Returns, Index Numbers, and Inflation

Nonparametric Tests

Filters

The formula for the confidence interval of the population variance σ² is valid only when the random sample is drawn from a ________ distributed population.

Which of the following is the formula for the sample variance s² when used as an estimate of σ² for a random sample of n observations from a population?

Statistical inference for σ² is based on the F distribution.

Consider the hypotheses H₀: σ² = 169, H_A: σ² ≠ 169. A sample variance of 98 is obtained from a random sample of 10 observations drawn from a normally distributed population. At 1% significance level, conduct a test for the population variance using the p-value approach.

The following are the competing hypotheses and the relevant summary statistics Η₀: / ≤ 1, Η_A: / > 1. Which of the following statements is correct, regarding the assumptions for conducting the hypothesis test?