1 Which of the following is correct a If the Pvalue computed

1.) Which of the following is correct

a. If the P-value computed from r is less than or equal to the significance level (), conclude that there is sufficient evidence to support a claim of a linear correlation. If theP-value computed from r is greater than the significance level () conclude there is not sufficient evidence to support a claim of a linear correlation.

b. If the P-value computed from r is greater than the significance level (), conclude that there is sufficient evidence to support a claim of a linear correlation. If the P-value computed from r is less than the significance level () conclude there is not sufficient evidence to support a claim of a linear correlation.

c. If the computed linear correlation coefficient r lies in the left tail beyond the leftmost critical value or if it lies in the right tail beyond the rightmost critical value, conclude that there sufficient evidence to support the claim of a linear correlation. If the computed linear correlation coefficient “r” lies between the two critical values, conclude that there is not sufficient evidence to support the claim of a linear correlation.

d.If the computed linear correlation coefficient r lies in the left tail beyond the leftmost critical value or if it lies in the right tail beyond the rightmost critical value, conclude that there is insufficient evidence to support the claim of a linear correlation. If the computed linear correlation coefficient “r” lies between the two critical values, conclude that there is sufficient evidence to support the claim of a linear correlation.

e. both a and c are correct

f. both b and d are correct

2.) You are analyzing a set of paired data and your linear correlation results were r = 0.591 and a P-value of .294 . The level of significance is .05 and the critical value from table a-6 was r = +/- 0.878.

What will be your conclusion?

a. there is sufficient evidence to support the conclusion that there is a linear correlation between the two variables

b. there is not sufficient evidence to support the conclusion that there is a linear correlation between the two variables

c. additional data is needed to make a conclusion

d. none of the above

3.) The value ____ is the proportion of the variation in y that is explained by the linear relationship between x and y.

a. x

b. y

c. r

d. r²

Solution

1.

P-value approach:

When p value is greater than level of significance, then we fail to reject the null hypothesis. That is result is not significant.

Critical value approach:

When r value lies between the critical value, then we fail to reject the null hypothesis. That is result is not significant.

Hence, option (a) and (c) both are correct. hence, option (e) is correct.

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2.

SInce P-value is greater than 0.05 and also r is lies between the critical values so we fail to reject the null hypothesis. So there is not sufficient evidence to support the conclusion that there is a linear correlation between the two variables. Hence, option B is correct.

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3.

The value of r-square is the proportion of the variation in y that is explained by the linear relationship between x and y. So option d is correct.