Hypothesis Testing for One – Sample Mean

So the t* test statistic is:

t* test statistic

4) Calculate the p-value

In order to determine the p-value, in addition to the t* test statistic above we also need to calculate the degrees of freedom. For our example, this is just the batch size subtracted by 1: 100 – 1 = 99.

The t* value 4.444 and the 99 degrees of freedom can be input into any statistical software or freely available web application to estimate the corresponding p-value of .000012.

5) Make a decision about the null hypothesis

As our p-value 0.000012 is much lower than the significance level 5% (aka 0.05) we reject the null hypothesis that company C’s CO2 mean is equal to the average value from different manufacturers.

6) State the overall conclusion

From the data given, at the significance level of 5% or the confidence level of 95%, we reject the null hypothesis in favor of the alternative, that company C’s cars’ CO2 emission is greater than the average value from different manufacturers.