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Chapter 14: Q14.123 (page 585)

For each exercise, decide at 10% significance level, whether the data provide sufficient evidence to reject the null hypothesis in favour of alternate hypothesis.

Ha:鈥�p鈮�0

Short Answer

Expert verified

We reject the null hypothesis Ha:鈥�p鈮�0, the variables are not linearly correlated.

Step by step solution

01

Correlation Coefficient 

Sample correlation coefficient is calculated by

r=鈭�zxzy/(鈥�n-1)鈥�

where zxn=(xn-xmean)/standarddeviation, and same for zyn

Using excel and above, r=-0.6325

02

Hypothesis Testing 

r鈮�0for sample needs to be tested using hypothesis testing, to ensure that the population correlation parameterp (rho) 鈮�0

t=r/(1-r2)鈥�/(n-2)=-0.6325/0.599/3=-0.6325/0.4468t=-1.415

As t value is smaller and p value is greater at two sided 0.10 significance level, so we accept the null hypothesis [H0:鈥�p=0]

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Most popular questions from this chapter

Gas Guzzlers. Use the data on the WeissStats site for gas mileage and engine displacement for 121 vehicles referred to in Exercise 14.41.

Explain why the predictor variable is useless as a predictor of the response variable if the slope of the population regression line is 0.

In Exercises 14.98-14.108, use the technology of your choice to do the following tasks.
a. Decide whether your can reasonably apply the conditional mean and predicted value t-interval procedures to the data. If so, then also do parts (b) - (h).
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%Te 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).

14.10 PCBs and Pelicans. The data from Exercise 14.40for shell thickness and concentration of PCBs of 60Anacapa pelican eggs are on the WeissStats site. Specified value of the predictor variable: 220ppm.

In Exercises 14.12-14.21, we repeat the data and provide the sample regression equations for Exercises 4.48 -4.57.

a. Determine the standard error of the estimate.

b. Construct a residual plot.

c. Construct a normal probability plot of the residuals.

y=1.75+0.25x

Following are the data on age of fetuses and length of crown-rump.use伪=0.10presuming that the assumption for regression inference are met, decide at the specified significance level whether the data provide sufficient evidence to conclude that the predictor variable is useful for providing the response variable.

See all solutions

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