he tollowing applies to Questions 1 - Suppose the Transportation Safety Board of

ID: 3048400 • Letter: H

Question

he tollowing applies to Questions 1 - Suppose the Transportation Safety Board of Canada wants to examine the safety of compact cars, midsize cars, and full size cars. The following table displays the pressure applied to the driver's head during a crash test for samples of cars of each type, along with some summary statistics: Compact Midsize Full-size 469 427 525 471 473 643 655 703 484 456 401 mean 667 447 std. dev. 31.75 40.17 42.23 An analysis of variance to compare the mean pressure applied to the driver's head for the three car types was conducted. Suppose that all necessary assumptions have been satisfied Question 1 (1 point) The overall mean response for the three car types is: (Report your final answer to one decimal place.) Your Answer: Answer Save Question 2 (1 point) we would like to conduct an analysis of variance at the 5% level of significance to compare the means of the three populations. Using Table 4, what is the critical value for the appropriate test of significance? (Report your final answer to two decimal places.) Your Answer: Answer Save Question 3 (1 point) In conducting the analysis of variance F test, we will commit a Type I error if we conclude that there is: O sufficient evidence that at least one of the population means differs from the others when in fact they are all equal o sufficient evidence that one of the population means differs from the others when in fact all four population means O insufficient evidence that at least one of the population means differs from the others even though this is the case O insufficient evidence that all three population means differ from each other even though this is the case O sufficient evidence that all three population means differ from each other when in fact they are all equal differ from each other

Explanation / Answer

Overall mean response = {(3 x 667) + (4 x 473) + (3 x 447)}/10

= 523.4 ANSWER

ANOVA TABLE

Source

Fcrit

p-value

Car Size

89534

44767.2

30.0682

4.7374

0.0004

Error

10422

1488.857

Total

99956

11106.27

Critical value = 4.74 ANSWER

Since Fcal > Fcrit, the null hypothesis of equal treatment effect is rejected at 5% level of significance.

=> there is enough evidence to suggest that mean pressure applied to the driver’s head are significantly different for the three car sizes.

DONE

Type I error corresponds to rejecting the null hypothesis when it is true. Since, in the present case, the null hypothesis is that mean pressure applied to the driver’s head are the same for the three car sizes, we will be committing Type I error if we conclude that there is

Sufficient evidence that at least one of the population means differs from the others when in fact they are all equal. ANSWER