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Chapter 14: Q 14.140 (page 586)

PCBs and Pelicans. The data from Exercise 14.40 for shell thickness and concentration of PCBs of 60 Anacapa pelican eggs are on the WeissStats site. Do the data provide sufficient evidence to conclude that concentration of PCBs and shell thickness are linearly correlated for Anacapa pelican eggs?

Short Answer

Expert verified

Hence, the correlation t-test procedure is not reasonable to apply for the given data.

Step by step solution

01

Step 1:Given information

The data from Exercise 14.40 for shell thickness and concentration of PCBs of 60 Anacapa pelican eggs are on the WeissStats site.

02

Step 2:Explaination

Check whether reasonably to apply the correlation t-test procedure to data by using Exercise 14.40.

- From the residual plot, it is clear that the residuals are fall in the horizontal band.

- From the normal probability plot of residuals, it is clear that the residuals are appears in the linear pattern.

Hence, the assumption 1-3 for the regression inferences is not violated for the variables thickness and PCB.

From Exercise 14.76, the data does not provide sufficient evidence to conclude that PCB is useful for predicting THICKNESS. Hence, it is not possible to use linear model to predict the variables.

Hence, the correlation t-test procedure is not reasonable to apply for the given data.

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Most popular questions from this chapter

In Exercises 14.70-14.80, use the technology of your choice to do the following tasks.

a. Decide whether you can reasonably apply the regression t-test. If so, then also do part (b).

b. Decide, at the 5%significance level, whether the data provide sufficient evidence to conclude that the predictor variable is useful for predicting the response variable.

14.70 Birdies and Score. The data from Exercise 14.34 for number of birdies during a tournament and final score for 63 women golfer are on the WeissStats site.

Find a 95%prediction interval for the value of the response variable corresponding to the specified value of the predictor variable.

Plant Emissions. Use the data on plant weight and quantity of volatile emissions from Exercise 14.25.

a. compute the standard error of the estimate and interpret your answer

b. interpret your result from part (a) if the assumptions for regression inferences hold.

c. obtain a residual plot and a normal probability plot of the residuals.

d. decide whether you can reasonably consider Assumptionsfor regression inferences to be met by the variables under consideration. (The answer here is subjective, especially in view of the extremely small sample sizes.)

Gas Guzzlers. The data from Exercise 14.41 for gas mileage and engine displacement of 121 vehicles are on the WeissStats site. Specified value of the predictor variable: 3.0L.

a. Decide whether you can reasonably apply the conditional mean and predicted value t-interval procedures to the data. If so, then also do parts (b)-(f).

b. Determine and interpret a point estimate for the conditional mean of the response variable corresponding to the specified value of the predictor variable.

c. Find and interpret a 95%confidence interval for the conditional mean of the response variable corresponding to the specified value of the predictor variable.

d. Determine and interpret the predicted value of the response variable corresponding to the specified value of the predictor variable.

e. Find and interpret a 95%prediction interval for the value of the response variable corresponding to the specified value of the predictor variable.

f. Compare and discuss the differences between the confidence interval that you obtained in part (c) and the prediction interval that you obtained in part (e).

Identify two graphs used in a residual analysis to check the Assumptions 1-3 for regression inferences, and explain the reasoning behind their use:
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