Finance

Q: In one-way ANOVA, a large value of F results when the within-treatment variability is large compared to the between-treatment variability.

Q: The error sum of squares measures the between-treatment variability.

Q: After rejecting the null hypothesis of equal treatments, a researcher decided to compute a 95 percent confidence interval for the difference between the mean of treatment 1 and mean of treatment 2 based on the Tukey procedure. At Î± = .05, if the confidence interval includes the value of zero, then we can reject the hypothesis that the two population means are equal.

Q: The 95 percent individual confidence interval for 1 - 2 (treatment mean 1 -treatment mean 2) will always be smaller than the Tukey 95 percent simultaneous confidence interval for 1 - 2.

Q: Experimental data are collected so that the values of the dependent variables are set before the values of the independent variable are observed.

Q: When using a randomized block design, the interaction effect between the block and treatment factors cannot be separated from the error term.

Q: The experimentwise for the 95 percent individual confidence interval for 1 - 2 (treatment mean 1 - treatment mean 2) will always be smaller than the experimentwise for a Tukey 95 percent simultaneous confidence interval for 1 - 2.

Q: In a completely randomized (one-way) ANOVA, with other things being equal, as the sample means get closer to each other, the probability of rejecting the null hypothesis decreases.

Q: A one-way analysis of variance is a method that allows us to estimate and compare the effects of several treatments on a response variable.

Q: If factors being studied cannot be controlled, the data are said to be observational.

Q: A vitamin-water manufacturer wants to compare the effects on sales of three water colors: green, blue, and red. Four regions are selected for the test, with the following ANOVA results.Source of Variation df SS MSEColor 2 243.25 121.63Region 3 354.00 118.00Interaction 6 189.75 Error 12 129.00 Total 23 916.00 If there is no interaction effect, test the individual null hypotheses on the effect of each factor on mean sales at = .01.

Q: A vitamin-water manufacturer wants to compare the effects on sales of three water colors: green, blue, and red. Four regions are selected for the test, with the following ANOVA results.Source of Variation df SS MSEColor 2 243.25 121.63Region 3 354.00 118.00Interaction 6 189.75 Error 12 129.00 Total 23 916.00 Compute the mean square and F to test the null hypothesis that there is no interaction at = .01.

Q: Consider a two-way analysis of variance experiment with treatment factors A and B. The results are summarized below.Source of Variation df SSFactor A 4 86Factor B 5 75Interaction 20 75Error 90 300Total 119 536Find an individual 95 percent confidence interval of the mean response of 25.1 obtained when using level 1 of factor A and level 2 of factor B.

Q: Consider a two-way analysis of variance experiment with treatment factors A and B. The results are summarized below.Source of Variation df SSFactor A 4 86Factor B 5 75Interaction 20 75Error 90 300Total 119 536If the mean response for level 1 of Factor A is 31.5 and the mean response for level 2 of Factor A is 22.5, calculate a Tukey simultaneous 95 percent confidence interval for this difference.

Q: Consider a two-way analysis of variance experiment with treatment factors A and B. The results are summarized below.Source of Variation df SSFactor A 4 86Factor B 5 75Interaction 20 75Error 90 300Total 119 536Compute the mean square and F, and test the null hypothesis that no interaction exists between factors A and B at = .05.

Q: Consider a two-way analysis of variance experiment with treatment factors A and B. The results are summarized below.Source of Variation df SSFactor A 4 86Factor B 5 75Interaction 20 75Error 90 300Total 119 536If there are an equal number of observations in each cell, what is the number of observations in each cell? (number of cells = level of factor A level of factor B)

Q: Consider a two-way analysis of variance experiment with treatment factors A and B, with factor A having four levels and factor B having three levels. The results are summarized below.Source of Variation df SSFactor A 71Factor B 63Interaction 50Error 280Total 71 446Compute the mean squares and appropriate F statistics to test the null hypotheses of no effect from either factor at = .05 (assumption: no interaction effect).

Q: Consider a two-way analysis of variance experiment with treatment factors A and B, with factor A having four levels and factor B having three levels. The results are summarized below.Source of Variation df SSFactor A 71Factor B 63Interaction 50Error 280Total 71 446Compute the mean squares and F to test the null hypothesis that no interaction exists between factor A and B at = .05.

Q: Consider a two-way analysis of variance experiment with treatment factors A and B, with factor A having four levels and factor B having three levels.The results are summarized below.Source of Variation df SSFactor A 71Factor B 63Interaction 50Error 280Total 71 446If there are an equal number of observations in each cell, what is the number of observations in each cell? (number of cells = level of factor A level of factor B)

Q: Consider a two-way analysis of variance experiment with treatment factors A and B, with factor A having four levels and factor B having three levels. The results are summarized below.Source of Variation df SSFactor A 71Factor B 63Interaction 50Error 280Total 71 446Calculate the degrees of freedom for the error term.

Q: Consider a two-way analysis of variance experiment with treatment factors A and B, with factor A having four levels and factor B having three levels. The results are summarized below.Source of Variation df SSFactor A 71Factor B 63Interaction 50Error 280Total 71 446Calculate the degrees of freedom for the interaction between Factors A and B.

Q: Consider a two-way analysis of variance experiment with treatment factors A and B, with factor A having four levels and factor B having three levels. The results are summarized below.Source of Variation df SSFactor A 71Factor B 63Interaction 50Error 280Total 71 446Calculate the degrees of freedom for factor A and factor B.

Q: Consider the following partial analysis of variance table from a randomized block design with 10 blocks and 6 treatments.Source SSTreatments 2,477.53Blocks 3,180.48Error 11,661.38Total Test H0: there is no difference between blocks at = .05.

Q: Consider the following partial analysis of variance table from a randomized block design with 10 blocks and 6 treatments.Source SSTreatments 2,477.53Blocks 3,180.48Error 11,661.38Total Calculate the degrees of freedom for the interaction between Factors A and B.

Q: In testing the difference between two means from two independent populations, the sample sizes do not have to be equal.

Q: There are two types of machines, called type A and type B. Both type A and type B can be used to produce a certain product. The production manager wants to compare efficiency of the two machines. He assigns each of the 15 workers to both types of machines to compare their hourly production rate. In other words, each worker operates machine A and machine B for one hour each. These two samples are independent.

Q: When comparing two independent population means, if n1 = 13 and n2 = 10, degrees of freedom for the t statistic is 22.

Q: In an experiment involving matched pairs, a sample of 12 pairs of observations is collected. The degrees of freedom for the t statistic is 10.

Q: In forming a confidence interval for 1 - 2, only two assumptions are required: independent samples and sample sizes of at least 30.

Q: When testing the difference between two proportions selected from populations with large independent samples, the z test statistic is used.

Q: An independent samples experiment is an experiment in which there is no relationship between the measurements in the different samples.

Q: We use the following data for a test of the equality of variances for two populations at = .10. Sample 1 is randomly selected from population 1 and sample 2 is randomly selected from population 2. Can we reject H0 at = .10?

Q: Testing H0: 12 22, HA: 12 > 22 at = .05, where n1 = 16, n2 = 19, s12 = .03, and s22 = .02, can we reject the null hypothesis?

Q: What is the F statistic for testing H0: 12 22, HA: 22 > 12 at = .05, where n1 = 16, n2 = 19, s12 = .03, and s22 = .02?

Q: When testing H0: 12 = 12, HA: 12 > 22 at = .01, where n1 = 5, n2 = 6, s12 = 15,750, and s22 = 10,920, what critical value do we use?

Q: Testing H0: 12 = 12, HA: 12 > 22 at = .01, where n1 = 5, n2 = 6, s12 = 15,750, and s22 = 10,920, can we reject the null hypothesis?

Q: What is the value of the F statistic for H0: 12 12, HA: 12 > 12, where s1 = 3.3 and s2 = 2.1?

Q: What is the value of the computed F statistic for testing equality of population variances where s12 = .004 and s22 = .002? Consider HA: 12 > 22.

Q: When testing H0: 12 22 and HA: 12 > 22, where s12 = .004, s22 = .002, n1 = 4, and n2 = 7 at = .05, what critical value do we use?

Q: When testing H0: 12 22 and HA: 12 > 22, where s12 = .004, s22 = .002, n1 = 4, and n2 = 7 at = .05, what is the decision on H0?Do not reject the null hypothesis.

Q: Two different firms design their own tests for business graduates, and an employer administers both versions to a random selection of prospective employees. Results are below. At = .02, test the claim that both versions produce the same score.Mean difference = -4.25Standard error of the difference = 1.411

Q: A test of driving ability is given to a random sample of 10 student drivers before and after they complete a formal driver education course. Results follow.Test the hypothesis that there is no difference between the before-class scores and the after-class scores at = .05.

Q: A test of driving ability is given to a random sample of 10 student drivers before and after they complete a formal driver education course. Results follow. Calculate the t statistic to test that there is no difference between the before-class scores and the after-class scores.

Q: A test of driving ability is given to a random sample of 10 student drivers before and after they complete a formal driver education course. Results follow. Calculate the mean difference between the before-class scores and the after-class scores.

Q: A test of driving ability is given to a random sample of 10 student drivers before and after they complete a formal driver education course. Results follow. Write the null and alternative hypotheses testing the claim that the test score is not affected by the course.

Q: Suppose that a realtor is interested in comparing the price of midrange homes in two cities in a midwestern state. She conducts a small survey in the two cities, looking at the price of midrange homes. Assume equal population variances. Calculate the 95 percent confidence interval.

Q: The registrar at a state college is interested in determining whether there is a difference of more than one credit hour between male and female students in the average number of credit hours taken during a term. She selected a random sample of 60 male and 60 female students and observed the following sample information.What do you conclude at = .01? Assume unequal variances.

Q: The registrar at a state college is interested in determining whether there is a difference of more than one credit hour between male and female students in the average number of credit hours taken during a term. She selected a random sample of 60 male and 60 female students and observed the following sample information.Calculate the test statistic to be used in the analysis. Assume unequal variances.

Q: The registrar at a state college is interested in determining whether there is a difference of more than one credit hour between male and female students in the average number of credit hours taken during a term. She selected a random sample of 60 male and 60 female students and observed the following sample information.Set up the alternative hypothesis to test the claim.

Q: A market research study conducted by a local winery on white wine preference found the following results. Of a sample of 500 men, 120 preferred white wine. Of a sample of 500 women, 210 preferred white wine. What do you conclude at = .05 about the claim that the proportion of women who prefer white wine is 25 percent higher than the proportion of men who prefer white wine?

Q: A market research study conducted by a local winery on white wine preference found the following results. Of a sample of 500 men, 120 preferred white wine. Of a sample of 500 women, 210 preferred white wine. Calculate the test statistic for testing the claim that the percentage of women preferring white wine is 25 percent higher than that of men.

Q: In a market research study conducted by a local winery on white wine preference, the following results were found. Of a sample of 500 men, 120 preferred white wine. Of a sample of 500 women, 210 preferred white wine. Set up the alternative hypothesis that will test the claim that the percentage of women who prefer white wine is 25 percent higher than the percentage of men who prefer white wine.

Q: A coffee shop franchise owner is looking at two possible locations for a new shop. To help him decide, he looks at the number of pedestrians that go by each of the two locations in one-hour segments. At location A, counts are taken for 35 one-hour units, with a mean number of pedestrians of 421 and a sample standard deviation of 122. At the second location (B), counts are taken for 50 one-hour units, with a mean number of pedestrians of 347 and a sample standard deviation of 85. Assume the two populations variances are not known but are equal. Testing the claim that both sites have the same mean number of pedestrians at = .01, what do you conclude?

Q: A coffee shop franchise owner is looking at two possible locations for a new shop. To help him decide, he looks at the number of pedestrians that go by each of the two locations in one-hour segments. At location A, counts are taken for 35 one-hour units, with a mean number of pedestrians of 421 and a sample standard deviation of 122. At the second location (B), counts are taken for 50 one-hour units, with a mean number of pedestrians of 347 and a sample standard deviation of 85. Assume the two population variances are not known but are equal. Set up the null hypothesis to test the claim that both sites have the same number of pedestrians.

Q: A coffee shop franchise owner is looking at two possible locations for a new shop. To help him decide, he looks at the number of pedestrians that go by each of the two locations in one-hour segments. At location A, counts are taken for 35 one-hour units, with a mean number of pedestrians of 421 and a sample standard deviation of 122. At the second location (B), counts are taken for 50 one-hour units, with a mean number of pedestrians of 347 and a sample standard deviation of 85. Assume the two population variances are not known but are equal. Calculate a 95 percent confidence interval for the difference in pedestrian traffic at the two locations.

Q: A coffee shop franchise owner is looking at two possible locations for a new shop. To help make a decision, he looks at the number of pedestrians that go by each of the two locations in one-hour segments. At location A, counts are taken for 35 one-hour units, with a mean number of pedestrians of 421 and a sample standard deviation of 122. At the second location (B), counts are taken for 50 one-hour units, with a mean number of pedestrians of 347 and a sample standard deviation of 85. Assume the two population variances are not known but are equal. Calculate the pooled estimate of 2.

Q: A test of mathematical ability is given to a random sample of 10 eighth-grade students before and after they complete a semester-long basic mathematics course. The mean score before the course was 119.60, and after the course the mean score was 130.80. The standard deviation of the difference is 16.061. What do you conclude at = .01? Use confidence intervals to draw your conclusion.

Q: A test of mathematical ability is given to a random sample of 10 eighth-grade students before and after they complete a semester-long basic mathematics course. The mean score before the course was 119.60, and after the course the mean score was 130.80. The standard deviation of the difference is 16.061. Calculate the test statistic to test the claim that scores were higher after the course.

Q: Two hospital emergency rooms use different procedures for triage of their patients. We want to test the claim that the mean waiting time of patients is the same for both hospitals. The 40 randomly selected subjects from hospital A produce a mean of 18.3 minutes. The 50 randomly selected patients from hospital B produce a mean of 25.31 minutes. Assume sa = 2.1 minutes and sb =2.92 minutes. What do you conclude about the waiting time for patients in the two hospitals, testing at = .001?

Q: Two hospital emergency rooms use different procedures for triage of their patients. We want to test the claim that the mean waiting time of patients is the same for both hospitals. The 40 randomly selected subjects from hospital A produce a mean of 18.3 minutes. The 50 randomly selected patients from hospital B produce a mean of 25.31 minutes. Assume sa = 2.1 minutes and sb = 2.92 minutes. Calculate the test statistic for testing the hypothesis that there is a difference in the mean waiting time between the two hospitals. Assume unequal variances.

Q: Two hospital emergency rooms use different procedures for triage of their patients. We want to test the claim that the mean waiting time of patients is the same for both hospitals. The 40 randomly selected subjects from hospital A produce a mean of 18.3 minutes. The 50 randomly selected patients from hospital B produce a mean of 25.31 minutes. Sample standard deviations are sa = 2.1 minutes and sb = 2.92 minutes. Set up the null hypothesis to determine whether there is a difference in the mean waiting time between the two hospitals.

Q: A marketing research company surveyed grocery shoppers on the East Coast and West Coast to find the percentage of the customers who prefer chicken to other meat. The data are given below. Determine the 95 percent confidence interval for the difference between the proportion of customers on the West Coast who prefer chicken and the proportion of customers on the East Coast who prefer chicken.

Q: A marketing research company surveyed grocery shoppers on the East Coast and West Coast to find the percentage of the customers who prefer chicken to other meat. The data are given below.What is the test statistic for the alternative hypothesis that the West Coast prefers chicken at a higher proportion than the East Coast?

Q: A marketing research company surveyed grocery shoppers on the East Coast and West Coast to find the percentage of the customers who prefer chicken to other meat. The data are given below.The marketing research company is testing the hypothesis that the proportion of customers who prefer chicken is higher on the West Coast. Test at = .05.

Q: A marketing research company surveyed grocery shoppers on the East Coast and West Coast to find the percentage of the customers who prefer chicken to other meat. The data are given below.The marketing research company is testing the hypothesis that the proportion of customers who prefer chicken is the same for the two regions. Test at = .10.

Q: Coach Z, the mid-distance running coach for the Olympic team of an eastern European country, claims that his six-month training program significantly reduces the average time to complete a 1500-meter run. Five mid-distance runners were randomly selected. Their times (in minutes) for the 1500-meter run were recorded before and after six months of training under Coach Z. The results are given below. Construct the appropriate 95 percent confidence interval when we want to test whether there is a difference (sd = .228).

Q: Coach Z, the mid-distance running coach for the Olympic team of an eastern European country, claims that his six-month training program significantly reduces the average time to complete a 1500-meter run. Five mid-distance runners were randomly selected. Their times (in minutes) for the 1500-meter run were recorded before and after six months of training under Coach Z. The results are given below. At an alpha level of .05, can we conclude that there has been a significant decrease in the mean time?

Q: Find a 95 percent confidence interval for the difference between the proportions of people who prefer cola versus root beer (RB), where cola = .21, RB = .12, ncola = 200, and nRB = 150.

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