Question

An agency examined the relationship between the ozone level (in parts per million or ppm) and the population (in Dependent variable is: Ozone millions) of cities. Part of the regression analysis is shown to the right. Complete parts a and b below. R squared-84.3% s 5.418 with 16-2 14 df Coeff 18.162 6.501 SE(Coeff) 2.098 2.093 Variable Intercept Population a) It is-suspected that the greater the population of a city, the higher its ozone level. Is the relationship statistically significant? Assuming the conditions for inference are satisfied, test an appropriate hypothesis and state your conclusion in context. Use a significance level of a0.05. State the null and altemative hypotheses. 。A. Ho: There is no linear relationship between population and ozone, p,-o A: There is a linear relationship between population and ozone. P Mo. 0 B. Ho: There is a posisve relationship between population and ozon, pi-o HA: There is a negative relationship between population and ozone, pi 0. Ho: There is a linear relationship between population and ozone, β HA: There is a negative relationship between population and ozone, β1 0 O c. Determine the t-test statissc. Round to two decimal places as needed.) Find the P-value. P-value (Round to four decimal places as needed.) What do you conclude? Reject Ho. These data do not provide evidence of a linear relationship between population and ozone. A. Reject Ho. These data provide evidence of a linear relationship between population and ozone. O B. O C. Fail to reject Ho These data do not provide evidence of a linear relationship between population and ozone. OD. Fail to reject Ho. These data provide evidence of a linear relationship between population and ozone lues of both R2 and s in your explanation. b) Do you think that the population of a city is a useful predictor of ozone level? Use the va tion accounts for 84.3% of the variability in ozone, and the residual standard deviation is only 5.418 parts per million. and the residual standard deviation is very large (5.418 parts per million). o A. Yes, populat O B. No, population accounts for 84.3% of the variability in ozone, ° C. . Yes, 0 D. No, population accounts for 84.3% of the variability in the residuals, and the residual standard error is 5 4 in the residuals, and the residual standard error is 5.418 times less than the ozone mean. population accounts for 84.3% of the variability Cirk to seleet vour answerls)

Answer 1

a)

option D is correct for hypothesis

t =coefficient/standard error =(6.501/2.093)=3.11

p value =0.0038 ( please try 0.0039 if this comes wrong)

Conclusion: option B

b)

option A is correct