Which of the following statements are true in hypothesis testing? I. If we fail

Question

Which of the following statements are true in hypothesis testing? I. If we fail to reject Ho when it is false, we made Type I error II. A small P-value indicates strong evidence to support H_0 III. We will reject H_0 if the test statistic is located in the rejection region a. I only b. II and III only c. III only d. I, II and III e. I and III only The equation of regression line between the variables x, and y is given by y = -3x + 2, and the correlation coefficient is calculated to be r = -0.95. Coefficient of determination r^2 = 0.9025. Which of the following statement(s) is (are) correct? The linear relationship between x and y is positive. 90.25% of the variation in y can be explained by linear relation between x and y. If x increase 1 unit, then y will increase 3 units If x = 5, one would predict that y = -13. a. Only 1 is true b. Only 2, 3 and 4 are true c. Only 2 and 4 are true d. Only 1 and 4 are true e. Only 2 and 3 are true

Explanation / Answer

Question 8:

I) Type I error is incorrect rejection of a true null hypothesis . Therefore this statement is false .

II) When the p-value is smaller then the level of significance, then the test is significant and we reject the null hypothesis. Therefore the given statement is false.

III) If the test statistic lies in the rejection region then the test is significant and we can reject the null hypothesis. Therefore the given statement is true here

Therefore only the third statement is true. Therefore c is the correct answer here.

Question 9:

1) As the correlation coefficient here is negative 0.95. Therefore the relationship between the 2 variables here is negative. Therefore the given statement is false here.

2) The coefficient of determination gives the percentage of the variation in y that can be explained by the linear relation between x and y. Therefore the given statement here is true.

3) As we are given that:

y = -3x + 2

Therefore when x increases by 1 unit, y decreases by 3 units as the coefficient is negative.

Therefore this statement is also false.

4) For x = 5, y = -3*5 + 2 = - 13

Therefore the given statement is true here.

Therefore statements 2 and 4 are correct. Therefore c is the correct answer here.

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