Exam 11: Two Sample Tests of Hypothesis

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 should have approximately equal standard deviations. iii. To employ ANOVA, the populations being studied must be approximately normally distributed.

Analysis of variance is used to:

Given the following Analysis of Variance table for three treatments each with six observations. What is the critical value of F at the 5% level of significance?

What distribution does the F distribution approach as the sample size increases?

i. The alternate hypothesis for ANOVA states that not all the means are equal. ii. For an ANOVA test, rejection of the null hypothesis does not identify which populations differ Significantly. iii. If the computed value of F is 4.01 and the critical value is 2.67, we would conclude that all 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 sum of squares of the error?

i. If we want to determine which treatment means differ, one method is confidence intervals. ii. If the confidence interval includes 0, there is a difference in the pair of treatment means. iii. If both end points of a confidence interval are of the same sign, it indicates that the treatment Means are not different.

Which one of the following is not assumed in the use of ANOVA?

i. The shape of the F distribution is determined by the degrees of freedom for the F-statistic, one for The numerator and one for the denominator. ii. The F distribution's curve is positively skewed. iii. Unlike Student's t distribution, there is only one F distribution.

If an ANOVA test is conducted and the null hypothesis is rejected, what does this indicate?

A preliminary study of hourly wages paid to unskilled employees in three metropolitan areas was Conducted. Seven employees were included from Area A, 9 from Area B and 12 from Area D The test statistic was computed to be 4.91. What can we conclude at the 0.05 level?

A large department store examined a sample of the 18 credit card sales and recorded the amounts Charged for each of three types of credit cards: MasterCard, Visa and American Express. Six MasterCard sales, seven Visa and five American Express sales were recorded. The store used ANOVA to test if the mean sales for each credit card were equal. What are the degrees of freedom For the F statistic?

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. The least number of sources of variation in ANOVA is two.

An ANOVA comparing the waiting times for four different emergency rooms shows the following Comparison of the four mean waiting times. Which two pairs of means are significantly different?

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 critical value of F at the 1% level of significance?

i. The test statistic used in ANOVA is F. ii. The calculated F value must be equal to or greater than zero (0). iii. The shape of the F distribution is symmetrical.

Random sample of executives from companies with assets over $1 million was selected and asked For their annual income and level of education. The following MegaStat output summarized the Results: Using this output, what conclusions can you draw?

A random sample of 30 executives from companies with assets over $1 million was selected and Asked for their annual income and level of education. The ANOVA comparing the average income Among three levels of education rejected the null hypothesis. The Mean Square Error (MSE) was 243)7. The following table summarized the results: Based on the comparison between the mean annual incomes for executives with Undergraduate And Master's Degree or more.

An electronics company wants to compare the quality of their cell phones to the cell phones from Three competitors. They sample 10 phones from each company and count the number of defects for Each phone. Using Excel, what test is used to compare the average number of defects?

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 mean square for error?