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Can we use ANOVA (analysis of variance) to analyze these data? Yes, because the

ID: 3062438 • Letter: C

Question

Can we use ANOVA (analysis of variance) to analyze these data?

Yes, because the response variable is quantitative and there are three or more groups of batteries.

No, because both the explanatory variable and the response variable are quantitative.

Yes, because ANOVA can be used whenever we have three or more populations being compared regardless of the type of response variable.

No, because even though there are four categories, the response variable is categorical.

2. Which of the following is the appropriate alternative hypothesis for the null hypothesis H0: a = b = c = d?

In this problem, a = mean time of Brand A, b = mean time of Brand B, etc.)

Ha: at least one of the means is different

Ha: none of the means are equal

Ha: a b c d

Ha: , a b, a c, a d, b c, b d, c d

3. In order to analyze the data with ANOVA, we need to satisfy the condition of independence. How do we know that this condition has been met?

One SRS of batteries is selected from a collection of batteries of all brands.

The batteries are randomly allocated to the four brands.

Separate random samples of batteries are selected from each brand.

4. After the battery times were measured, we obtained these dot plots.

On the basis of these dot plots, is the condition of normality of populations met?

Yes, because the dot plots show no extreme skewness and no outliers.

Yes, because each of the populations are known to be normally distributed.

No, because at least one of the dot plots show extreme skewness and/or some outliers.

No, because the sample sizes were not big enough to apply the central limit theorem.

5. Here are the ANOVA results.

Is the condition of equal population standard deviation met?

No, because (largest standard deviation) / (smallest standard deviation) is greater than 2

Yes, because (largest standard deviation) / (smallest standard deviation) is less than 2

No, because the largest standard deviation is greater than 2

Yes, because the largest standard deviation is less than 2

6. According to the output, what is the F-statistic value for this test?

365.28

264.50

0.000

121.76

16.57

7. Assume all the conditions of this test have been met. Using the p-value from the output, what can we conclude at = 0.01?

Reject the null hypothesis and conclude that at least one mean differs from the other means.

Fail to reject the null hypothesis and conclude that there is insufficient evidence to say that the means are not all equal.

Fail to reject the null hypothesis and conclude that at least one mean differs from the other means.

Reject the null hypothesis and conclude that there is insufficient evidence to say that the means are not all equal.

8. Assume all the conditions of this test have been met. On the basis of the confidence intervals given in the output, which brand has a mean time that is significantly higher than the means of the other three brands?

Brand A

Brand B

Brand C

Brand D

9. On the basis of the confidence interval plots given in the output, the mean life for Brand B batteries is significantly greater than the mean life for Brand A batteries.

True

False

10. In order to perform an analysis of variance (ANOVA), the response variable must be quantitative.

True

False

Yes, because the response variable is quantitative and there are three or more groups of batteries.

No, because both the explanatory variable and the response variable are quantitative.

Yes, because ANOVA can be used whenever we have three or more populations being compared regardless of the type of response variable.

No, because even though there are four categories, the response variable is categorical.

2. Which of the following is the appropriate alternative hypothesis for the null hypothesis H0: a = b = c = d?

In this problem, a = mean time of Brand A, b = mean time of Brand B, etc.)

Ha: at least one of the means is different

Ha: none of the means are equal

Ha: a b c d

Ha: , a b, a c, a d, b c, b d, c d

3. In order to analyze the data with ANOVA, we need to satisfy the condition of independence. How do we know that this condition has been met?

One SRS of batteries is selected from a collection of batteries of all brands.

The batteries are randomly allocated to the four brands.

Separate random samples of batteries are selected from each brand.

4. After the battery times were measured, we obtained these dot plots.

On the basis of these dot plots, is the condition of normality of populations met?

Yes, because the dot plots show no extreme skewness and no outliers.

Yes, because each of the populations are known to be normally distributed.

No, because at least one of the dot plots show extreme skewness and/or some outliers.

No, because the sample sizes were not big enough to apply the central limit theorem.

5. Here are the ANOVA results.

Is the condition of equal population standard deviation met?

No, because (largest standard deviation) / (smallest standard deviation) is greater than 2

Yes, because (largest standard deviation) / (smallest standard deviation) is less than 2

No, because the largest standard deviation is greater than 2

Yes, because the largest standard deviation is less than 2

6. According to the output, what is the F-statistic value for this test?

365.28

264.50

0.000

121.76

16.57

7. Assume all the conditions of this test have been met. Using the p-value from the output, what can we conclude at = 0.01?

Reject the null hypothesis and conclude that at least one mean differs from the other means.

Fail to reject the null hypothesis and conclude that there is insufficient evidence to say that the means are not all equal.

Fail to reject the null hypothesis and conclude that at least one mean differs from the other means.

Reject the null hypothesis and conclude that there is insufficient evidence to say that the means are not all equal.

8. Assume all the conditions of this test have been met. On the basis of the confidence intervals given in the output, which brand has a mean time that is significantly higher than the means of the other three brands?

Brand A

Brand B

Brand C

Brand D

9. On the basis of the confidence interval plots given in the output, the mean life for Brand B batteries is significantly greater than the mean life for Brand A batteries.

True

False

10. In order to perform an analysis of variance (ANOVA), the response variable must be quantitative.

True

False

Brand D Brand C. : Brand B Brand A 40 Time 50

Explanation / Answer

right choices are

(1) Yes, because the response variable is quantitative and there are three or more groups of batteries.

(2) Ha: at least one of the means is different

(3)Separate random samples of batteries are selected from each brand.

(4)Yes, because the dot plots show no extreme skewness and no outliers.

(5) Yes, because (largest standard deviation) / (smallest standard deviation) is less than 2

(6)16.57

(7)Reject the null hypothesis and conclude that at least one mean differs from the other means.

(8) Brand D, since its interval doesnot touch other brand interval

(9)False, since confidence interval of A and B touches each other

(10)True

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