An agency examined the relationship between the ozone level (in parts per million or ppm) and the population (in millions) of cities. Part of the regression analysis is shown to the right. Complete parts a and b below.
Dependent variable is: Ozone R squared= 85.8% s= 5.137 with 16-2=14 df
Variable Coeff SE (Coeff)
Intercept 18.206 2.013
Population 6.987 1.915
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 alphaequals0.05. State the null and alternative hypotheses.
A. Upper H 0: There is a linear relationship between population and ozone, beta 1not equals0. Upper H Subscript Upper A: There is a negative relationship between population and ozone, beta 1less than0.
B. Upper H 0: There is no linear relationship between population and ozone, beta 1equals0. Upper H Subscript Upper A: There is a positive relationship between population and ozone, beta 1greater than0.
C. Upper H 0: There is no linear relationship between population and ozone, beta 1equals0. Upper H Subscript Upper A: There is a linear relationship between population and ozone, beta 1not equals0.
D. Upper H 0: There is a positive relationship between population and ozone, beta 1greater than0. Upper H Subscript Upper A: There is a negative relationship between population and ozone, beta 1less than0.
Determine the t-test statistic.
t=___ (Round to two decimal places as needed.)
Find the P-value.
P-value=____(Round to four decimal places as needed.)
What do you conclude?
A. Fail to reject Upper H 0. These data do not provide evidence of a linear relationship between population and ozone.
B. Reject Upper H 0. These data do not provide evidence of a linear relationship between population and ozone.
C. Reject Upper H 0. These data provide evidence of a linear relationship between population and ozone.
D. Fail to reject Upper H 0. These data provide evidence of a linear relationship between population and ozone.
b) Do you think that the population of a city is a useful predictor of ozone level? Use the values of both Upper R squared and s in your explanation.
A. Yes, population accounts for 85.8% of the variability in the residuals, and the residual standard error is 5.137 times less than the ozone mean.
B. Yes, population accounts for 85.8% of the variability in ozone, and the residual standard deviation is only 5.137 parts per million.
C. No, population accounts for 85.8% of the variability in the residuals, and the residual standard error is 5.137 times greater than the ozone mean.
D. No, population accounts for 85.8% of the variability in ozone, and the residual standard deviation is very large (5.137 parts per million).
a.)
B.)
H0: There is no linear relationship between population and ozone,
H A: There is a positive relationship between population and ozone,
now
Test Statistic(t)=6.987/1.915 =3.65
degree of freedom=14
p-value= 0.0013
ans: C. Reject H0. These data provide evidence of a linear relationship between population and ozone.
ans:B. Yes, The population accounts for 84.1% of the variabilty in ozone and the residual standard deviation is only 5.789 ppm.
Get Answers For Free
Most questions answered within 1 hours.