Question

3. An oil additive for automobiles claims that it increases fuel mileage by at least a mean of 2.3 mpgwith a standard deviation of .5 mpg. A group of AP Statistics students decide to test this claim. They randomly select 49 people to test the oil additive and found that drivers using the additive increased their fuel mileage by a mean of 2.1 mpg, with a standard deviation of .5. Is this sufficient evidence to reject the null hypothesis in favor of the manufacturer’s claim? Use α = 0.01 Use the four step process for Hypothesis Testing. (8 points)

Step 1 – State Hypothesis in context of the problem.

Step 2 – Gather data, check assumptions, and find rejection region using α.

Step 3 – Calculate the appropriate test statistic and p-value.

Step 4 – State conclusion in context of the problem.

Step 1

Step 2

Step 3

Step 4

Answer 1

Lets consider the question,

Step 1 : Null hypothesis : Ho : = 2.3

Step 2 : Alternative hypothesis : Ha : 2.3

Step 3 : Perform 1 sample Z test because population standard deviation is known

One-Sample Z

Test of mu = 2.3 vs not = 2.3
The assumed standard deviation = 0.5

N Mean SE Mean 99% CI Z P
49 2.10000 0.07143 (1.91601, 2.28399) -2.80 0.005

Step 4 : Since p value (.005) is less than .01 we reject the null hypothesis and conclude that adding additive does not increase mileage to 2.3. In fact it is less than 2.3.