Question 1

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 2

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 question asks whether the test statistic for testing whether the two populations have equal variances is F=1.3733, which implies a hypothesis test for equal variances. Since the problem does not provide a significance level or degrees of freedom, we cannot perform a formal hypothesis test. However, we can compare the test statistic F=1.3733 to the critical value from an F-distribution with appropriate degrees of freedom and determine whether we would reject or fail to reject the null hypothesis of equal variances. Without this information, we cannot say definitively whether the statement is true or false.

Question 3

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 4

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 5

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

Using the formula for the chi-square test statistic for a single population variance, we have (n-1)*S^2/σ^2 = 34.79. Substituting the given values, we get (n-1)*600/345 = 34.79, which simplifies to (n-1) = 0.063. Solving for n, we get n = 1.063, which means that the sample size must be approximately 21.

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

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 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 ounces.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

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

We need to test the null hypothesis that the population variance of the amount of filling in burritos is less than or equal to 1.7 ounces, against the alternative hypothesis that it is greater than 1.7 ounces. This is a right-tailed test. The test statistic is calculated as (n-1)*s^2/sigma^2, where s^2 is the sample variance, sigma^2 is the hypothesized population variance (1.7 ounces), and n is the sample size. Substituting the given values, we get a test statistic of 16.63. The critical value for a right-tailed test at 0.10 level of significance with 17 degrees of freedom (n-1) is 10.645. Since the test statistic (16.63) is greater than the critical value (10.645), we reject the null hypothesis and conclude that the standards are not being met.

Question 10

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 11

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 calculated as the ratio of the sample variances and since both variances are always non-negative, the F test statistic is always positive.

Question 12

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

Accepted Answer

The F-distribution is used to test the hypotheses about the equality of two population variances.

Question 13

If a hypothesis test for a single population variance is to be conducted using a significance level of to 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 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, which gives x² = 22.3071.

Question 14

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 test statistic to compare the standard deviations of two independent samples can be calculated using the formula:

test statistic = (s1^2/s2^2) / Fα/2,v1,v2

where s1 and s2 are the sample standard deviations of the two samples, v1 and v2 are the sample sizes of the two samples, and Fα/2,v1,v2 is the critical value of the F-distribution with degrees of freedom v1 and v2 at the α/2 significance level.

Plugging in the given values, we have:

s1 = 180
s2 = 80
v1 = 14
v2 = 8
α = 0.05

From the F-distribution table, the critical value at α/2 = 0.025 with v1 = 14 and v2 = 8 degrees of freedom is 3.172.

Therefore, the test statistic is:

test statistic = (180^2/80^2) / 3.172 = 1.5394

The closest choice to this value is C.

Question 15

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 16

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 population variance, the test statistic is computed using the formula (n-1)*S^2/σ^2, which follows a chi-square distribution with n-1 degrees of freedom. Therefore, the correct choice is B.

Question 17

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 inches.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 inches.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 18

A potato chip manufacturer has found that in the past the standard deviation of bag weight has been 0.2 ounces.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 19

Sample A has a sample size of 15 and a standard deviation of 4.Sample B has a sample size of 30 and a standard deviation of 6.Both samples were taken from the same population.The 95 percent confidence interval estimate for the standard deviation of the population based on sample A will be ________ that based on sample B.

Accepted Answer

The confidence interval for the standard deviation of the population is inversely proportional to the square root of the sample size. Therefore, the confidence interval based on sample A will be narrower than that based on sample B because sample A has a smaller sample size.

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