Question

1.)

Explain what the​ P-value means in the given context.

The federal guideline for smog is​ 12% pollutants per​ 10,000 volume of air. A metropolitan city is trying to bring its smog level into federal guidelines. The city comes up with a new policy where city employees are to use city transportation to and from work. A local environmental group does not think the city is doing enough and that no real decrease in pollution will occur. An independent​ agency, hired by the​ city, conducts a test to determine if the​ city's strategy lessens the smog rate and concludes that the P-value=0.055. What is reasonable to conclude about the new strategy using alpha=​0.05?

a.) If the smog rate has not changed, there is a 5.5% chance of the new policy having no effect on smog.

b.) The probability that the new policy is effective in reducing the smog level is 0.055, assuming the null hypothesis is true.

c.) Assuming the smog rate has not changed, there is a 5.5% chance of obtaining the results found by the agency or even more extreme results. With alpha= 0.05, there is not enough evidence to claim that the new policy is effective in reducing smog.

d.) If the smog rate has not changed, there is a 94.5% chance of the new policy having no effect on smog.

e.) Assuming the smog rate has not changed, there is a 5.5% chance of obtaining the results found by the agency or even more extreme results. With alpha=0.05, we can conclude that the new policy is effective in reducing smog.

Answer 1

Let mu be the smog level before the new policy

mu1 be the smog level after the new policy being implemented

Null Hypothesis => mu1=mu

Alternate Hypothesis => mu1<mu

Under Null hypothesis, p value =0.055 which is less than alpha = 0.05 => we fail to reject null Hypothesis => No sufficient evidence to reject the claim that smog level is decreased significantly

=> 5.5 % chance that H0 is true is random => assuming that smog rate has not changed, there are 5.5 % chance of obtaining the results found by the agency or more mixture results. Since, we have failed to reject null hypothesis, it means there are not sufficient evidence that new policy is effective in reducing smog

So option C