(1) state the null and alternative hypotheses,
(2) select a level of significance,
(3) select the test statistics,
(4) formulate the decision rule,
(5) compute the value of test statistic, and
(6) make a decision.
Consider the following hypotheses:
| H_{o} / mu = 250
H_{o} : mu ne250
Scenario 2.
An oil company claims that their new gasoline formula contains an additive that results in increase fuel efficiency. To test this claim, the collaborate with an automobile company to send 30 identical cars to do a road trip from Manila to Dau. The average mileage of these cars turned out to be 10.8km/L. Without the additive, it is known that these cars' average mileage is 10km/L with standard deviation of 1.4km/L. At 0.01 level of significance, should we agree with the company's claim?
(2) select a level of significance,
(3) select the test statistics,
(4) formulate the decision rule,
(5) compute the value of test statistic, and
(6) make a decision.
Consider the following hypotheses:
| H_{o} / mu = 250
H_{o} : mu ne250
Scenario 2.
An oil company claims that their new gasoline formula contains an additive that results in increase fuel efficiency. To test this claim, the collaborate with an automobile company to send 30 identical cars to do a road trip from Manila to Dau. The average mileage of these cars turned out to be 10.8km/L. Without the additive, it is known that these cars' average mileage is 10km/L with standard deviation of 1.4km/L. At 0.01 level of significance, should we agree with the company's claim?
Answers & Comments
Answer:
1. Null hypothesis: The mean mileage of the cars using the new gasoline formula is equal to or less than 10 km/L.
Alternative hypothesis: The mean mileage of the cars using the new gasoline formula is greater than 10 km/L.
H0: μ ≤ 10
Ha: μ > 10
2. The level of significance is 0.01.
3. Since the sample size is greater than 30 and the population standard deviation is known, we can use a z-test.
4. The decision rule is to reject the null hypothesis if the calculated z-score is greater than the critical z-value obtained from the z-table at the 0.01 level of significance.
5. The test statistic is given by:
z = (x̄ - μ) / (σ/√n)
where x̄ is the sample mean, μ is the hypothesized population mean, σ is the population standard deviation, and n is the sample size.
z = (10.8 - 10) / (1.4/√30) = 3.08
6. The calculated z-score of 3.08 is greater than the critical z-value of 2.33 obtained from the z-table at the 0.01 level of significance. Therefore, we reject the null hypothesis and conclude that there is evidence to support the company's claim that their new gasoline formula results in an increase in fuel efficiency.