Fuel Consumption and Cars
Biodiesel fuel has a cloud point, the temperature at which the fuel becomes cloudy, of approximately 13°C. This clouding can lead to poor engine performance and can even cause an engine to stop completely. An industrial chemical company produces an additive designed to lower the cloud point of this type of fuel. A random sample of six different biodiesel fuels was obtained and the cloud point was measured for each. One ounce of the chemical additive was mixed in with every fuel sample and the cloud point was measured again. The resulting data are given in the following table (temperatures in °C).
|
Fuel
|
1
|
2
|
3
|
4
|
5
|
6
|
|
Before additive
|
11.7
|
12.9
|
14.2
|
12.7
|
11.3
|
12.4
|
|
After additive
|
10.3
|
10.7
|
14.1
|
10.0
|
11.2
|
12.1
|
a. Assume normality, and conduct the appropriate hypothesis test to determine whether the additive lowers the mean cloud point in biodiesel fuel. Use a = 0.05.
b. Conduct an inappropriate two-sample t test to compare the population mean cloud point before treatment with the population mean cloud point after treatment. Assume the population variances are unequal and use a = 0.05.
c. Compare the conclusions in parts (a) and (b). How are the test statistics the same, and how do they differ?