Question 1

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 2

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, which are both positive values. Therefore, the F test statistic will always be positive.

Question 3

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:

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

Question 4

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 5

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

Accepted Answer

When conducting a hypothesis test regarding a population variance, the test statistic is calculated as x² from the chi-square distribution, where x is the sample variance, u is the hypothesized population variance, n is the sample size, and P0 is the level of significance. Therefore, the best choice for the test statistic is option B.

Question 6

To test the following hypotheses at the 0.05 level of significance,using a sample size of n = 15. H₀ : σ² = 0.05 H_A : σ² ≠ 0.05 What is the upper tail critical value?

Accepted Answer

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

Question 7

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 answer of A consulting report that was recently submitted...

Question 8

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 9

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 10

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.

Question 11

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:

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

Question 12

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 test statistic F is used to test the hypothesis of equal variances between two populations. The null hypothesis is that the populations have equal variances, and the alternative hypothesis is that they do not. In this case, the calculated value of F is 1.3733, which is not greater than the critical value at any common significance level. Therefore, we fail to reject the null hypothesis and conclude that there is no significant difference between the variances of the two populations at a given level of significance.

Question 13

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 14

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

The test statistic for variance is calculated using the chi-square distribution. Given the sample variance of 2.89 and the desired variance of 1.7, the test statistic is greater than the critical value at a 0.10 significance level, indicating that the standards are not being met.

Question 15

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 16

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 17

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

Accepted Answer

The appropriate null hypothesis when testing whether two population variances are equal is that they are equal, so the null hypothesis should be represented as H0: σ12 = σ22. Option A is the only one that represents this null hypothesis correctly. Option B represents the alternative hypothesis, which is that the variances are not equal. Options C and D represent one-tailed hypotheses, which are not appropriate for testing equal variances.

Question 18

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.

Question 19

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

For a chi-square test for a single population variance with n = 16 and a significance level of 0.10 for an upper-tail test, the critical value is found using the chi-square distribution table. With 15 degrees of freedom (n-1), the critical value is approximately 22.3071.

Question 20

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

To test the hypothesis that the standard deviation of University A is greater than the standard deviation of University B, we can use the F-test. The test statistic for the F-test is calculated as the ratio of the variances of the two samples. In this case, we have:
Sample A: n1=14, variance s1^2 = 225.62
Sample B: n2=8, variance s2^2 = 50.50
The test statistic is therefore:
F = s1^2 / s2^2 = 225.62 / 50.50 = 4.472
The degrees of freedom for the F-test are (n1-1) and (n2-1), which are 13 and 7 in this case. Using a table of F-distributions or a calculator, we can find that the critical value of F at alpha=0.05 and degrees of freedom 13 and 7 is 3.046. Since our calculated F-value of 4.472 is greater than the critical value of 3.046, we reject the null hypothesis and conclude that the standard deviation of University A is indeed greater than the standard deviation of University B.

Quiz 11: Hypothesis Tests and Estimation for Population Variances