Question 1

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

Accepted Answer

CHISQ.DIST.RT

Question 2

Statistical inference for σ² is based on the F distribution.

Accepted Answer

Statistical inference for variance (σ^2) typically involves the Chi-square (χ^2) distribution, not the F distribution. The F distribution is primarily used for comparing two variances.

Question 3

The null hypothesis H₀: σ² ≤ is rejected if the value of the test statistic exceeds .

Accepted Answer

This statement follows the general rule for rejecting null hypotheses - if the test statistic exceeds the critical value, the null hypothesis is rejected.

Question 4

Use the R function ________ to obtain left-tail probabilities of the chi-square distribution.

Accepted Answer

The answer of Use the R function ________ to obtain...

Question 5

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

Accepted Answer

The answer of The values of the  distribution range...

Question 6

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

Accepted Answer

The population variance is commonly used to measure the risk of investments, as it provides a measure of how much the returns of an investment vary from their average or expected value.

Question 7

The skewness of the chi-square distribution depends on the degrees of freedom.

Accepted Answer

The skewness of the chi-square distribution increases as the degrees of freedom decrease.

Question 8

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.

Accepted Answer

The formula for constructing the confidence interval for the ratio of two population variances assumes that the samples are drawn from normally distributed populations. This is a requirement for using the F-distribution, which underlies the confidence interval calculation for variance ratios.

Question 9

In general, the  distribution is the probability distribution of the sum of several independent squared standard ________ random variables.

Accepted Answer

The answer of In general, the  distribution is the...

Question 10

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

Accepted Answer

The answer of Inference for two population variances is done...

Question 11

The estimator of  /  used in the inference regarding the ratio of two population variances is  /  .

Accepted Answer

The answer of The estimator of  /  used...

Question 12

The  distribution is negatively skewed.

Accepted Answer

The answer of The  distribution is negatively skewed....

Question 13

A right-tailed test for the ratio of two population variances Η₀: / ≤ 1 examines whether is greater than .

Accepted Answer

The null hypothesis for a right-tailed test of the ratio of two population variances is that the ratio is less than or equal to 1. Therefore, if the alternative hypothesis is that the ratio is greater than 1, then the test is a right-tailed test. This means that the p-value will represent the probability that the ratio is greater than the null value of 1. So, if the p-value is less than the chosen significance level, we would reject the null hypothesis and conclude that the ratio is significantly greater than 1.

Question 14

The value of the test statistic for the hypothesis test of the population variance, σ² is computed as = .

Accepted Answer

The format of the test statistic indicates that it is a hexadecimal number, and the use of underscores suggests that it is written in Microsoft Office's "Equation Editor." Therefore, it is likely that the test statistic was calculated using software or a calculator, rather than being made up.

Question 15

For a test about the ratio of two population variances, the test statistic is given by  /  .

Accepted Answer

The test statistic for the ratio of two population variances follows an F distribution, and the numerator and denominator degrees of freedom are calculated based on the sample sizes of the two populations. The format of the given test statistic suggests that it is calculated based on these degrees of freedom, therefore it is true that the test statistic for the ratio of two population variances is given by this expression.

Question 16

The relevant value in the ________ tail of the  distribution is  .

Accepted Answer

The answer of The relevant value in the ________ tail...

Question 17

It is preferable to place the smaller sample variance in the numerator of the statistic.

Accepted Answer

The answer of It is preferable to place the smaller...

Question 18

The formula for the confidence interval of the population variance σ² is valid for the random samples drawn from any population.

Accepted Answer

The formula for the confidence interval of the population variance assumes that the population from which the sample is drawn follows a normal distribution. For populations that do not follow a normal distribution, the formula may not be valid or accurate.

Question 19

The sampling distribution of / is the χ² distribution.

Accepted Answer

The numerator and denominator of the fraction represent chi-square distributions with degrees of freedom equal to the number of parameters estimated in each model, respectively. The ratio of two chi-square distributions with nonnegative degrees of freedom follows a F-distribution, not a chi-square distribution. Therefore, the statement is false.

Question 20

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

Accepted Answer

The answer of The formula for the confidence interval of...

Quiz 11: Statistical Inference Concerning Variance

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

Statistical inference for σ2 is based on the F distribution.

The null hypothesis H0: σ2 ≤ is rejected if the value of the test statistic exceeds .

Use the R function ________ to obtain left-tail probabilities of the chi-square distribution.

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

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

The skewness of the chi-square distribution depends on the degrees of freedom.

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.

In general, the distribution is the probability distribution of the sum of several independent squared standard ________ random variables.

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

The estimator of / used in the inference regarding the ratio of two population variances is / .

The distribution is negatively skewed.

A right-tailed test for the ratio of two population variances Η0: / ≤ 1 examines whether is greater than .

The value of the test statistic for the hypothesis test of the population variance, σ2 is computed as = .

For a test about the ratio of two population variances, the test statistic is given by / .

The relevant value in the ________ tail of the distribution is .