Question 1

When a hypothesis test is to be conducted regarding a population variance, the test statistic will be:

Accepted Answer

The correct test statistic for a hypothesis test regarding a population variance is an x2 value from the chi-square distribution. This is because the chi-square distribution is used when dealing with variance and standard deviation parameters in a population.

Question 2

It is believed that the SAT scores for students entering two state universities may have different standard deviations. Specifically, it is believed that the standard deviation at University A is greater than the standard deviation at University B. To test this using an alpha = 0.05 level, a sample of 14 student SAT scores from University A was selected and a sample of 8 SAT scores from University B was selected. The following sample results were observed:  Based on this information, what is the value of the test statistic?

Accepted Answer

The answer of It is believed that the SAT scores...

Question 3

The F test statistic for testing whether the variances of two populations are the same is always positive.

Accepted Answer

The F test statistic is the ratio of two sample variances, and since variance is always non-negative, the F statistic is always positive.

Question 4

Which of the following is the appropriate null hypothesis when testing whether two population variances are equal?

Accepted Answer

The answer of Which of the following is the appropriate...

Question 5

There is interest at the American Savings and Loan as to whether there is a difference between average daily balances in checking accounts that are joint accounts (two or more members per account) versus single accounts (one member per account). To test this, a random sample of checking accounts was selected with the following results:  Based upon these data, if tested using a significance level equal to 0.10, the assumption of equal population variances should be rejected.

Accepted Answer

The answer of There is interest at the American Savings...

Question 6

It is believed that the SAT scores for students entering two state universities may have different standard deviations. Specifically, it is believed that the standard deviation at University A is greater than the standard deviation at University B. If a statistical test is to be conducted, which of the following would be the proper way to formulate the null hypothesis?

Accepted Answer

The answer of It is believed that the SAT scores...

Question 7

A fast food restaurant that sells burritos is concerned about the variability in the amount of filling that different employees place in the burritos. To achieve product consistency it needs this variability to be no more than 1.7 ounces. A sample of n = 18 burritos showed a sample variance of 2.89 ounces. Using a 0.10 level of significance, what can you conclude?

Accepted Answer

To test if the variability in the amount of filling exceeds 1.7 ounces, we use the chi-square test for variance. The null hypothesis $H_0$ would state that the population variance $\sigma^2$ is less than or equal to 1.7 ounces^2, and the alternative hypothesis $H_a$ would state that the population variance is greater than 1.7 ounces^2. The test statistic is calculated using the formula $\chi^2 = \frac{(n-1)s^2}{\sigma_0^2}$, where $n$ is the sample size, $s^2$ is the sample variance, and $\sigma_0^2$ is the variance under the null hypothesis. Given $n = 18$ and $s^2 = 2.89$, and testing against $\sigma_0^2 = 1.7$, the test statistic would be greater than the critical value at the 0.10 level of significance, indicating that the null hypothesis should be rejected. This means the variability in the amount of filling is significantly greater than the standard allows, hence the standards are not being met.

Question 8

A potato chip manufacturer has found that in the past the standard deviation of bag weight has been 0.2 ounce. They want to test whether the standard deviation has changed. The null hypothesis is:

Accepted Answer

The answer of A potato chip manufacturer has found that...

Question 9

To test the following hypotheses at the 0.05 level of significance, using a sample size of n = 15.  What is the upper tail critical value?

Accepted Answer

The answer of To test the following hypotheses at the...

Question 10

A manufacturer of industrial plywood has a contract to supply a boat maker with a large amount of plywood. One of the specifications calls for the standard deviation in thickness to not exceed .03 inch. A sample of n = 30 sheets was sampled randomly from a recent production run. The mean thickness was right at the 3/4 inch target thickness and the sample standard deviation was .05 inch. Testing at the 0.05 level of significance, which of the following is true?

Accepted Answer

The answer of A manufacturer of industrial plywood has a...

Question 11

An analyst plans to test whether the standard deviation for the time it takes bank tellers to provide service to customers exceeds the standard of 1.5 minutes. The correct null and alternative hypotheses for this test are:

Accepted Answer

The answer of An analyst plans to test whether the...

Question 12

When conducting a one-tailed hypothesis test of a population variance using a sample size of n = 24 and a 0.10 level of significance, the critical value is:

Accepted Answer

The critical value for a one-tailed hypothesis test of a population variance with a sample size of n = 24 (which means degrees of freedom = 23) and a 0.10 level of significance can be found using the chi-square distribution table. For a 0.10 level of significance and 23 degrees of freedom, the critical value is closest to 32.0069.

Question 13

If a hypothesis test for a single population variance is to be conducted using a significance level of 0.10, a sample size of n = 16, and the test is a one-tailed upper-tail test, the critical value is:

Accepted Answer

The answer of If a hypothesis test for a single...

Question 14

The Russet Potato Company has been working on the development of a new potato seed that is hoped to be an improvement over the existing seed that is being used. Specifically, the company hopes that the new seed will result in less variability in individual potato length than the existing seed without reducing the mean length. To test whether this is the case, a sample of each seed is used to grow potatoes to maturity. The following information is given: 
The correct null hypothesis for testing whether the variability of the new seed is less than the old seed is:

Accepted Answer

The answer of The Russet Potato Company has been working...

Question 15

If the variance of the contents of cans of orange juice is significantly more than 0.003, the manager has to order to stop the filling machine. A sample of 26 cans of orange juice showed a standard deviation of 0.06 ounce. Based on the sample and at the 0.05 level of significance, the filling machine should be

Accepted Answer

The answer of If the variance of the contents of...

Question 16

Which distribution is used in testing the hypotheses about the equality of two population variances?

Accepted Answer

The F-distribution is used in testing hypotheses about the equality of two population variances. This is because the ratio of two independent sample variances, each divided by their respective degrees of freedom, follows an F-distribution under the null hypothesis that the population variances are equal.

Question 17

It is believed that the SAT scores for students entering two state universities may have different standard deviations. Specifically, it is believed that the standard deviation at University A is greater than the standard deviation at University B. To test this using an alpha = 0.05 level, a sample of 14 student SAT scores from University A was selected and a sample of 8 SAT scores from University B was selected. The following sample results were observed:  Based on this information, what is the critical value that will be used to test the hypothesis?

Accepted Answer

The answer of It is believed that the SAT scores...

Question 18

A consulting report that was recently submitted to a company indicated that a hypothesis test for a single population variance was conducted. The report indicated that the test statistic was 34.79, the hypothesized variance was 345 and the sample variance 600. However, the report did not indicate what the sample size was. What was it?

Accepted Answer

The sample size can be calculated using the formula:n = (s^2 / σ^2) * χ^2(1-α/2, v)where:s^2 is the sample varianceσ^2 is the hypothesized varianceχ^2(1-α/2, v) is the critical value of the chi-squared distribution with v degrees of freedom and a significance level of α/2In this case, we have:s^2 = 600σ^2 = 345χ^2(1-α/2, v) = 34.79We do not know the value of α, so we cannot calculate the exact value of n. However, we can approximate the value of n by using a significance level of 0.05. This gives us:n ≈ (600 / 345) * 34.79 ≈ 21

Question 19

There is interest at the American Savings and Loan as to whether there is a difference between average daily balances in checking accounts that are joint accounts (two or more members per account) versus single accounts (one member per account). To test this, a random sample of checking accounts was selected with the following results:  Based upon these data, the test statistic for testing whether the two populations have equal variances is F = 1.3733.

Accepted Answer

The answer of There is interest at the American Savings...

Question 20

If a hypothesis test for a single population variance is to be conducted, which of the following statements is true?

Accepted Answer

All the statements are true regarding a hypothesis test for a single population variance: A) correctly identifies that the null hypothesis is stated in terms of the population variance, B) correctly notes that the chi-square distribution is used in this context, and C) is incorrect in suggesting that increasing the sample size increases the critical value; in fact, increasing the sample size generally makes the test more sensitive (i.e., able to detect smaller differences) without necessarily changing the critical values, which are determined by the chosen level of significance and the degrees of freedom (which are indeed affected by sample size but not in a way that directly increases critical values as implied). My explanation contains an error regarding statement C, which might have led to confusion. Let's correct that: The critical value in the context of hypothesis testing, especially with chi-square distributions, is determined by the level of significance and the degrees of freedom (which are indeed affected by sample size). However, the relationship between sample size and critical values is not as directly stated in option C. The critical values for a given level of significance are determined by the distribution and the degrees of freedom, which for a chi-square test, depend on the sample size minus one. However, the statement as phrased in C about the critical value increasing with sample size for a given level of significance is misleading in this context. The correct understanding is that while sample size affects the degrees of freedom, and thus indirectly influences the distribution used to determine critical values, it does not directly cause an increase in critical values in the manner suggested.

Quiz 11: Hypothesis Tests and Estimation for Population Variances

When a hypothesis test is to be conducted regarding a population variance, the test statistic will be:

The F test statistic for testing whether the variances of two populations are the same is always positive.

Which of the following is the appropriate null hypothesis when testing whether two population variances are equal?

A potato chip manufacturer has found that in the past the standard deviation of bag weight has been 0.2 ounce. They want to test whether the standard deviation has changed. The null hypothesis is:

To test the following hypotheses at the 0.05 level of significance, using a sample size of n = 15. What is the upper tail critical value?

An analyst plans to test whether the standard deviation for the time it takes bank tellers to provide service to customers exceeds the standard of 1.5 minutes. The correct null and alternative hypotheses for this test are:

When conducting a one-tailed hypothesis test of a population variance using a sample size of n = 24 and a 0.10 level of significance, the critical value is:

If a hypothesis test for a single population variance is to be conducted using a significance level of 0.10, a sample size of n = 16, and the test is a one-tailed upper-tail test, the critical value is:

Which distribution is used in testing the hypotheses about the equality of two population variances?

If a hypothesis test for a single population variance is to be conducted, which of the following statements is true?