Question

A car manufacturer wants to test whether a new prototype engine meets air pollution standards. To seek certification by the Environmental Protection Agency (EPA) for compliance with emission standards, the manufacturer needs to submit convincing data. According to the federal standard, the average CO2 emission rate must be less than 20 parts per million (ppm) by volume. Ten new engines were made for testing purposes, and the carbon dioxide emission level of each was measured. The data (in ppm) were collected and given as follows:

{15.6, 16.2, 22.5, 20.5, 16.4, 19.4, 16.6, 17.9, 12.7, and 13.9}.

Is there significant evidence (at α = 0.01) supporting that the new engine meets the CO2 emission standard? **please show work/formulas used**

Answer 1

Steps:
1. Select population characteristics of interest: population mean = 20 ppm
2. Significance level = 0.01
3. Null hypothesis: H0=20 ppm
4. Alternate hypothesis: Ha not equal to 20 ppm
5. Calculate t statistic
6. Select acceptable region: t value between 3.25 to -3.25 for 9 degrees of freedom

Average = 17.17
Stdev = 2.98

So we need to find the significance using student’s t test by using the formula,
‘t=(sample mean-population)/sample standard deviation/sqrt of observation
= (17.17-20)/(2.98/sqrt(10))
= - 3.001

As the critical value at 0.01 significance for 9 degrees of freedom is 3.25 to -3.25 and the calculated t value falls in the critical region, we accept the null hypothesis and reject the alternate hypothesis,stating the new engine meets the Co2 emissions