12. Which of the following statements is TRUE In the linear regression model y =

Question

12. Which of the following statements is TRUE In the linear regression model y = At Ax + ', the error term represents random deviation from the line and is Normally distributed with mean 1 and var!ance 2 A. B. The correlation between x and y sr 0.10. If we multiply 5 to all x values and add 0.6 to all y values then the new correlation becomes 0.5 × 0.10 + 0.6 = 1.1. C. It is always good practice to assess the fit of a line to (x,y) data by examining the correlation r, R2, and residual plots The intercept Ro in the model y = in x. D. + Ax + measures the average change in y for every unit change The probability that an automobile tire has a flaw on it is 0.07. Randomly select 4 tires from the production line. What is the probability that exactly 2 out of the 4 tires both have flaws on them? A 0.0049 B. 0.0254 C. 0.225 D. 0.8649 13. 14, Out of n-1250 tiles, x = 98 tiles are cracked. what sample size needed so that a 2-sided 99% confidence interval for p has a margin of error of E-00157 A. 33 B. 749 C. 1233 D. 2138 Let p the true proportion of all such tiles that are cracked. A 90% confidence interval for is given by (-oo, 5.1). If we test Ho: -5 against Ha :

Explanation / Answer

Question12

(a) statement is false as mean of the error term is 0 not 1 as given in the proble.

(b) Statement is false as correlation value doesn't change when we multiply or divide.

(c) THe statement is true here.  NO explained required.

(d) The statement is false. As that is the defiinition of B1 not B0 .

Question 13

Pr(A tire has flaw) = 0.07

Pr(X = 2) = BIN (X = 2; 4) = 4C2 (0.07)2 (0.93)2 = 0.02543 {option B is correct]

Question 14

Here sample proportion p^ = 98/1250 = 0.0784

Margin of error = critical test statistic * standard error of proportion

for 99% confidence interval critical test statistic = 2.58

0.015 = 2.58 * sqrt [0.0784 * 0.9216/N]

N = 2138

Question 15

H0 : = 5

Ha : < 5

Retain H0 at the alpha = 0.05 level. option D is correct.

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