A major car manufacturer wants to test a new catalytic converter to determine whether it meets new air pollution standards.The mean emission of all converters of this type must be less than 20 parts per million of carbon.Ten (10)converters are manufactured for testing purposes and their emission levels are measured with a mean of 17.17 and a standard deviation of 2.98.Calculate the appropriate test statistic to test the hypotheses.
A)3.00
B)9.50
C)-0.95
D)-3.00
E)-9.50

Question

Quizplus · Accepted Answer

The appropriate test statistic to use is a one-sample t-test since we have a sample size of 10 and the population standard deviation is unknown.

We can calculate the t-value as:

t = (sample mean - hypothesized population mean) / (standard error of the mean)
standard error of the mean = standard deviation / sqrt(sample size)

t = (17.17 - 20) / (2.98 / sqrt(10))
t = -3.00

The calculated t-value is -3.00, which falls in the rejection region of the t-distribution with 9 degrees of freedom (df=10-1) at a significance level of 0.05. Therefore, we reject the null hypothesis that the mean emission of all converters of this type is less than or equal to 20 parts per million of carbon.

A Major Car Manufacturer Wants to Test a New Catalytic