Question 1

The random variable for a chi-square distribution may assume

Accepted Answer

The random variable for a chi-square distribution can only assume positive values because it is the sum of squared deviations from the mean.

Question 2

A sample of 21 observations yielded a sample variance of 16. If we want to test H₀: $\sigma$² = 16, the test statistic is

Accepted Answer

The test statistic for testing the variance is calculated using the formula: $(n-1)s^2/\sigma^2$, where $n$ is the sample size, $s^2$ is the sample variance, and $\sigma^2$ is the hypothesized population variance. Here, $(21-1) \times 16 / 16 = 20$.

Question 3

The symbol used for the variance of the population is

Accepted Answer

B

Question 4

The chi-square values (for interval estimation) for a sample size of 21 at 95% confidence are

Accepted Answer

The answer of The chi-square values (for interval estimation) for...

Question 5

The symbol used for the variance of the sample is

Accepted Answer

The variance of the sample is denoted by S².

Question 6

We are interested in testing whether the variance of a population is significantly less than 1.44. The null hypothesis for this test is

Accepted Answer

The null hypothesis should state that the population variance is greater than or equal to 1.44, as we are testing if it is significantly less than 1.44.

Question 7

The producer of a certain medicine claims that their bottling equipment is very accurate and that the standard deviation of all their filled bottles is 0.1 ounce or less. A sample of 20 bottles showed a standard deviation of 0.11. The test statistic to test the claim is

Accepted Answer

The answer of The producer of a certain medicine claims...

Question 8

To avoid the problem of not having access to Tables of F distribution with values given for the lower tail, the numerator of the test statistic should be the one with

Accepted Answer

The F distribution is skewed, and the test statistic is calculated as the ratio of two variances. To ensure the test statistic falls in the upper tail, the numerator should have the larger sample variance.

Question 9

The manager of the service department of a local car dealership has noted that the service times of a sample of 15 new automobiles has a standard deviation of 4 minutes. A 95% confidence interval estimate for the variance of service times for all their new automobiles is

Accepted Answer

The confidence interval for the variance is calculated using the chi-square distribution. With a sample size of 15, the degrees of freedom is 14. Using the chi-square values for 95% confidence, the interval for the variance is calculated as 8.576 to 39.796.

Question 10

A sample of 41 observations yielded a sample standard deviation of 5. If we want to test H₀: $\sigma$² = 20, the test statistic is

Accepted Answer

The test statistic for testing the variance is calculated using the formula: $(n-1)s^2/\sigma^2$. Here, $n = 41$, $s = 5$, and $\sigma^2 = 20$. So, the test statistic is $(41-1) \times 5^2 / 20 = 50$.

Question 11

A sample of 51 elements is selected to estimate a 95% confidence interval for the variance of the population. The chi-square values to be used for this interval estimation are

Accepted Answer

The answer of A sample of 51 elements is selected...

Question 12

A random sample of 31 charge sales showed a sample standard deviation of $50. A 90% confidence interval estimate of the population standard deviation is

Accepted Answer

We use the chi-square distribution with degrees of freedom equal to n-1 (30 degrees of freedom in this case) and the chi-square values from the table to construct the confidence interval. Using the formula:
(sample standard deviation)^2 * (n-1) / chi-square value
we get the following:

Lower limit: (50)^2 * 30 / 43.77 = 1,577.66
Upper limit: (50)^2 * 30 / 22.04 = 2,587.54

Therefore, the 90% confidence interval estimate of the population standard deviation is 41.39 to 63.68.

Question 13

A sample of n observations is taken from a population. The appropriate chi-square distribution has

Accepted Answer

The chi-square distribution used in statistical tests, such as the chi-square goodness-of-fit test or the chi-square test of independence, typically has n - 1 degrees of freedom, where n is the number of observations or categories.

Question 14

The manager of the service department of a local car dealership has noted that the service times of a sample of 30 new automobiles has a standard deviation of 6 minutes. A 95% confidence interval estimate for the standard deviation of the service times for all their new automobiles is

Accepted Answer

The confidence interval for the standard deviation is calculated using the chi-square distribution. Given a sample standard deviation of 6 minutes and a sample size of 30, the 95% confidence interval for the population standard deviation is approximately 4.778 to 8.066.

Question 15

A sample of 20 cans of tomato juice showed a standard deviation of 0.4 ounces. A 95% confidence interval estimate of the variance for the population is

Accepted Answer

The answer of A sample of 20 cans of tomato...

Question 16

The bottler of a certain soft drink claims their equipment to be accurate and that the variance of all filled bottles is 0.05 or less. The null hypothesis in a test to confirm the claim would be written as

Accepted Answer

The null hypothesis should reflect the claim being tested. Since the claim is that the variance is 0.05 or less, the null hypothesis is $\sigma^2 \le 0.05$.

Question 17

We are interested in testing to see if the variance of a population is less than 7. The correct null hypothesis is

Accepted Answer

The correct null hypothesis for testing variance is that the population variance is equal to or greater than the test value. In this case, the test value is 7. Therefore, the null hypothesis is S >= 7. Choice A has the symbol for population standard deviation, not variance. Choice C and D do not include the test value of 7.

Question 18

The value of F_.05 with 8 numerator and 19 denominator degrees of freedom is

Accepted Answer

We can use F-distribution tables or a calculator to find the value of F_.05. Using a calculator, we can input the degrees of freedom and the significance level to find the value of the F-statistic: F_.05 = F(8,19) at α = 0.05 = 2.48 Therefore, the answer is A.

Question 19

For an F distribution, the number of degrees of freedom for the numerator

Accepted Answer

The degrees of freedom for the numerator and denominator in an F distribution can vary independently; they can be larger, smaller, or equal to each other.

Question 20

The producer of a certain bottling equipment claims that the variance of all their filled bottles is 0.027 or less. A sample of 30 bottles showed a standard deviation of 0.2. The p-value for the test is

Accepted Answer

The sample standard deviation is 0.2, which gives a sample variance of 0.04. Using a chi-square test for variance with 29 degrees of freedom, the calculated chi-square statistic is higher than expected under the null hypothesis, leading to a p-value between 0.025 and 0.05.

Quiz 11: Inferences About Population Variances

The random variable for a chi-square distribution may assume

A sample of 21 observations yielded a sample variance of 16. If we want to test H₀: $\sigma$ ² = 16, the test statistic is

The symbol used for the variance of the population is

The chi-square values (for interval estimation) for a sample size of 21 at 95% confidence are

The symbol used for the variance of the sample is

We are interested in testing whether the variance of a population is significantly less than 1.44. The null hypothesis for this test is

The producer of a certain medicine claims that their bottling equipment is very accurate and that the standard deviation of all their filled bottles is 0.1 ounce or less. A sample of 20 bottles showed a standard deviation of 0.11. The test statistic to test the claim is

To avoid the problem of not having access to Tables of F distribution with values given for the lower tail, the numerator of the test statistic should be the one with

The manager of the service department of a local car dealership has noted that the service times of a sample of 15 new automobiles has a standard deviation of 4 minutes. A 95% confidence interval estimate for the variance of service times for all their new automobiles is

A sample of 41 observations yielded a sample standard deviation of 5. If we want to test H₀: $\sigma$ ² = 20, the test statistic is

A sample of 51 elements is selected to estimate a 95% confidence interval for the variance of the population. The chi-square values to be used for this interval estimation are

A random sample of 31 charge sales showed a sample standard deviation of $50. A 90% confidence interval estimate of the population standard deviation is

A sample of n observations is taken from a population. The appropriate chi-square distribution has

The manager of the service department of a local car dealership has noted that the service times of a sample of 30 new automobiles has a standard deviation of 6 minutes. A 95% confidence interval estimate for the standard deviation of the service times for all their new automobiles is

A sample of 20 cans of tomato juice showed a standard deviation of 0.4 ounces. A 95% confidence interval estimate of the variance for the population is

The bottler of a certain soft drink claims their equipment to be accurate and that the variance of all filled bottles is 0.05 or less. The null hypothesis in a test to confirm the claim would be written as

We are interested in testing to see if the variance of a population is less than 7. The correct null hypothesis is

The value of F_.05 with 8 numerator and 19 denominator degrees of freedom is

For an F distribution, the number of degrees of freedom for the numerator

The producer of a certain bottling equipment claims that the variance of all their filled bottles is 0.027 or less. A sample of 30 bottles showed a standard deviation of 0.2. The p-value for the test is

Quiz 11: Inferences About Population Variances

The random variable for a chi-square distribution may assume

A sample of 21 observations yielded a sample variance of 16. If we want to test H0: σ\sigmaσ 2 = 16, the test statistic is

The symbol used for the variance of the population is

The chi-square values (for interval estimation) for a sample size of 21 at 95% confidence are

The symbol used for the variance of the sample is

We are interested in testing whether the variance of a population is significantly less than 1.44. The null hypothesis for this test is

The producer of a certain medicine claims that their bottling equipment is very accurate and that the standard deviation of all their filled bottles is 0.1 ounce or less. A sample of 20 bottles showed a standard deviation of 0.11. The test statistic to test the claim is

To avoid the problem of not having access to Tables of F distribution with values given for the lower tail, the numerator of the test statistic should be the one with

The manager of the service department of a local car dealership has noted that the service times of a sample of 15 new automobiles has a standard deviation of 4 minutes. A 95% confidence interval estimate for the variance of service times for all their new automobiles is

A sample of 41 observations yielded a sample standard deviation of 5. If we want to test H0: σ\sigmaσ 2 = 20, the test statistic is

A sample of 51 elements is selected to estimate a 95% confidence interval for the variance of the population. The chi-square values to be used for this interval estimation are

A random sample of 31 charge sales showed a sample standard deviation of $50. A 90% confidence interval estimate of the population standard deviation is

A sample of n observations is taken from a population. The appropriate chi-square distribution has

The manager of the service department of a local car dealership has noted that the service times of a sample of 30 new automobiles has a standard deviation of 6 minutes. A 95% confidence interval estimate for the standard deviation of the service times for all their new automobiles is

A sample of 20 cans of tomato juice showed a standard deviation of 0.4 ounces. A 95% confidence interval estimate of the variance for the population is

The bottler of a certain soft drink claims their equipment to be accurate and that the variance of all filled bottles is 0.05 or less. The null hypothesis in a test to confirm the claim would be written as

We are interested in testing to see if the variance of a population is less than 7. The correct null hypothesis is

The value of F.05 with 8 numerator and 19 denominator degrees of freedom is

For an F distribution, the number of degrees of freedom for the numerator

The producer of a certain bottling equipment claims that the variance of all their filled bottles is 0.027 or less. A sample of 30 bottles showed a standard deviation of 0.2. The p-value for the test is

A sample of 21 observations yielded a sample variance of 16. If we want to test H₀: $\sigma$ ² = 16, the test statistic is

A sample of 41 observations yielded a sample standard deviation of 5. If we want to test H₀: $\sigma$ ² = 20, the test statistic is

The value of F_.05 with 8 numerator and 19 denominator degrees of freedom is