Question 1

The sampling distribution of the ratio of two sample variances $S _ { 1 } ^ { 2 }$ / $S _ { 2 } ^ { 2 }$ is said to be F-distributed provided that:

Accepted Answer

A)  the samples are independent. 
B)  the populations are normal with equal variances. 
C)  the samples are dependent and their sizes are large. 
D)  the samples are independently drawn from two normal populations. 
A)  the samples are independent. 
B)  the populations are normal with equal variances. 
C)  the samples are dependent and their sizes are large. 
D)  the samples are independently drawn from two normal populations.

Question 2

Random samples from two normal populations produced the following statistics: s1 = 3 n1=30
S2 = 4 n2=30
What is the value of the test statistic if we wanted to test the hypothesis that the two populations differ?

Accepted Answer

A) 0.750 
B) 1.333 
C) 1.778 
D) 0.563 
A) 0.750 
B) 1.333 
C) 1.778 
D) 0.563

Question 3

The value in an F-distribution with $v _ { 1 } = 4$ and $v _ { 2 } = 8$ degrees of freedom such that the area to its left is 0.975 is 5.05.

Accepted Answer

A) True 
 B)False

Question 4

In a random sample of 20 patients who visited the emergency room of hospital 1, a researcher found that the variance of the waiting time (in minutes) was 128.0. In a random sample of 15 patients in the emergency room of hospital 2, the researcher found the variance to be 178.8.
Can we infer at the 5% level of significance that the population variances differ?

Accepted Answer

@#LAT-DLM& 1. @#LAT-DLM& 1.
Rejection region: F >

Question 5

A study wants to investigate whether the population variance is greater than 8, if a random sample of size 40, yielded a variance of 10. Which of the following is the correct value of the test statistic?

Accepted Answer

A) 50 
B) 1.25 
C) 48.75 
D) 31.2 
A) 50 
B) 1.25 
C) 48.75 
D) 31.2

Question 6

Which of the following statements is false?

Accepted Answer

A)  The chi-squared distribution is positively skewed. 
B)  The chi-squared distribution is symmetrical. 
C)  All the values of the chi-squared distribution are positive. 
D)  The shape of the chi-squared distribution depends on the number of degrees of freedom. 
A)  The chi-squared distribution is positively skewed. 
B)  The chi-squared distribution is symmetrical. 
C)  All the values of the chi-squared distribution are positive. 
D)  The shape of the chi-squared distribution depends on the number of degrees of freedom.

Question 7

The value in an F-distribution with $v _ { 1 } = 6$ and $v _ { 2 } = 9$ degrees of freedom such that the area to its right is 0.05 is 3.37.

Accepted Answer

A) True 
 B)False

Question 8

The value in a chi-squared distribution with 5 degrees of freedom such that the area to its right is 0.10 is 1.61031.

Accepted Answer

A) True 
 B)False

Question 9

The value in a chi-squared distribution with 6 degrees of freedom such that the area to its left is 0.05 is 12.5916.

Accepted Answer

A) True 
 B)False

The sampling distribution of the ratio of two sample variances $S _ { 1 } ^ { 2 }$ / $S _ { 2 } ^ { 2 }$ is said to be F-distributed provided that:

Random samples from two normal populations produced the following statistics: s₁= 3 n₁=30 S₂ = 4 n₂=30 What is the value of the test statistic if we wanted to test the hypothesis that the two populations differ?

The value in an F-distribution with $v _ { 1 } = 4$ and $v _ { 2 } = 8$ degrees of freedom such that the area to its left is 0.975 is 5.05.

A study wants to investigate whether the population variance is greater than 8, if a random sample of size 40, yielded a variance of 10. Which of the following is the correct value of the test statistic?

Which of the following statements is false?

The value in an F-distribution with $v _ { 1 } = 6$ and $v _ { 2 } = 9$ degrees of freedom such that the area to its right is 0.05 is 3.37.

The value in a chi-squared distribution with 5 degrees of freedom such that the area to its right is 0.10 is 1.61031.

The value in a chi-squared distribution with 6 degrees of freedom such that the area to its left is 0.05 is 12.5916.

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Methods Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference: Introduction

Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Analysis of Variance

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Techniques

Statistical Inference: Conclusion

Time-Series Analysis and Forecasting

Index Numbers

Decision Analysis

Filters

Exam 15: Inference About Population Variances

The sampling distribution of the ratio of two sample variances S12S _ { 1 } ^ { 2 }S12​ / S22S _ { 2 } ^ { 2 }S22​ is said to be F-distributed provided that:

Random samples from two normal populations produced the following statistics: s1 = 3 n1=30 S2 = 4 n2=30 What is the value of the test statistic if we wanted to test the hypothesis that the two populations differ?

The value in an F-distribution with v1=4v _ { 1 } = 4v1​=4 and v2=8v _ { 2 } = 8v2​=8 degrees of freedom such that the area to its left is 0.975 is 5.05.

A study wants to investigate whether the population variance is greater than 8, if a random sample of size 40, yielded a variance of 10. Which of the following is the correct value of the test statistic?

Which of the following statements is false?

The value in an F-distribution with v1=6v _ { 1 } = 6v1​=6 and v2=9v _ { 2 } = 9v2​=9 degrees of freedom such that the area to its right is 0.05 is 3.37.

The value in a chi-squared distribution with 5 degrees of freedom such that the area to its right is 0.10 is 1.61031.

The value in a chi-squared distribution with 6 degrees of freedom such that the area to its left is 0.05 is 12.5916.

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Methods Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference: Introduction

Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Analysis of Variance

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Techniques

Statistical Inference: Conclusion

Time-Series Analysis and Forecasting

Index Numbers

Decision Analysis

Filters

The sampling distribution of the ratio of two sample variances $S _ { 1 } ^ { 2 }$ / $S _ { 2 } ^ { 2 }$ is said to be F-distributed provided that:

Random samples from two normal populations produced the following statistics: s₁= 3 n₁=30 S₂ = 4 n₂=30 What is the value of the test statistic if we wanted to test the hypothesis that the two populations differ?

The value in an F-distribution with $v _ { 1 } = 4$ and $v _ { 2 } = 8$ degrees of freedom such that the area to its left is 0.975 is 5.05.

The value in an F-distribution with $v _ { 1 } = 6$ and $v _ { 2 } = 9$ degrees of freedom such that the area to its right is 0.05 is 3.37.