Exam 11: Two Sample Tests of Hypothesis

In a study of low tar cigarettes, five cigarettes from each of three brands were tested to see if the Mean amount of tar per cigarette differs among the brands. i. The F critical value for alpha = 0.05 is 3.89. ii. If F calculated is 4.75, the decision if α = 0.05 is to reject H0. iii. If the calculated F is 4.74, the decision if α = 0.01 is to not reject H0.

i. If the computed value of F is 0.99 and the critical value is 3.89, we would not reject the null Hypothesis. ii. When comparing two population variances we use the F distribution. iii. A one way ANOVA is use to compare several treatment means.

Two accounting professors decided to compare the variation of their grading procedures. To Accomplish this they each graded the same 10 exams with the following results: At the 1% level of significance, what is the decision?

Given the following Analysis of Variance table for three treatments each with six observations. What is the mean square for treatments?

i. To employ ANOVA, the populations need not have equal standard deviations. ii. To employ ANOVA, the populations being studied need not be normally distributed. iii. A technique that is efficient when simultaneously comparing more than two population means is Known as analysis of deviation.

i. The alternate hypothesis for ANOVA states that not all the means are equal. ii. Not rejecting the null hypothesis in ANOVA indicates that the population means are equal. iii. The null hypothesis for an ANOVA is µ1 - µ2 = µ3.

A random sample of 25 executives from companies with assets over $1 million was selected and Asked for their annual income and level of education. The following Excel printout summarized the Results:

Two accounting professors decided to compare the variation of their grading procedures. To Accomplish this they each graded the same 10 exams with the following results: The calculated F ratio is:

Given the following Analysis of Variance table for three treatments each with six observations. What are the degrees of freedom for the numerator and denominator?

i. For the population means, the alternate hypothesis used in the analysis of variance test states that Μ1 = µ2 = µ3. ii. For an ANOVA test, rejection of the null hypothesis does not identify which populations differ Significantly. iii. The null hypothesis for an ANOVA is µ1 - µ2 = µ3.

In a study of low tar cigarettes, five cigarettes from each of three brands were tested to see if the Mean amount of tar per cigarette differs among the brands. i. The F critical value for alpha = 0.05 is 3.74. ii. If F calculated is 4.75, the decision if α = 0.05 is to reject H0. iii. If the calculated F is 4.74, the decision if α = 0.01 is to reject H0.

i. The statistical technique used to test the equality of three or more population means is called Analysis of variance (ANOVA). ii. To employ ANOVA, the populations need not have equal standard deviations. iii. To employ ANOVA, the populations being studied must be approximately normally distributed.

i. To employ ANOVA, the populations should have approximately equal standard deviations. ii. To employ ANOVA, the populations being studied must be approximately normally distributed. iii. A technique that is efficient when simultaneously comparing more than two population means is Known as analysis of variance (ANOVA).

i. For the population means, the alternate hypothesis used in the analysis of variance test states that Μ1 = µ2 = µ3. ii. For an ANOVA test, rejection of the null hypothesis does not identify which populations differ Significantly. iii. Not rejecting the null hypothesis in ANOVA indicates that the population means are equal.

A manufacturer of automobile transmissions uses three different processes. The management Ordered a study of the production costs to see if there is a difference among the three processes. A Summary of the findings is shown below. What is the calculated F?

In a study of low tar cigarettes, five cigarettes from each of three brands were tested to see if the Mean amount of tar per cigarette differs among the brands. i. There are 2 degrees of freedom for the numerator. ii. There are 14 degrees of freedom for the denominator. iii. If the sum of squares for the brands is 0.07, the mean square for brands is 0.035.

The F test statistic is the ratio of the:

Two accounting professors decided to compare the variation of their grading procedures. To Accomplish this they each graded the same 10 exams with the following results: What is the critical value of F at the 0.05 level of significance?

Suppose a package delivery company purchased 14 trucks at the same time. Five trucks were purchased from manufacturer A, four from B and five from manufacturer C. The cost of maintaining each truck was recorded. The company wants to test if the mean maintenance cost for trucks from each manufacturer were equal. Using Excel, what test would be used?

i. One characteristic of the F distribution is that computed F can only range between -1 and +1. ii. The F distribution's curve is positively skewed. iii. Like Student's t distribution, a change in the degrees of freedom causes a change in the shape of The F distribution.