Question 169:

Asked on April 25, 2008

Tags: t-statistic , Null Hypothesis , Alternative Hypothesis , Z-Statistic , 1-sample t-test

1

Answer:

No answer provided yet.

1. The null hypothesis is that there is no difference between the sample mean of 25C (from 60 readings).
2. The alternative hypothesis is that there is a difference between the sample and the estimated population mean temperature.
3. The sample size is large enough that you could use the Z-statistic, I prefer sticking with the t-statistic because as n gets larger the two approach each other. My approach is the more conservative since it will generate a slightly higher margin of error around the sample mean. In this example it won't make much difference.

So we're testing whether the observed mean of 25C could come from the same population with a mean of 23C (we're assuming both have the same standard deviation of 1.5C).

Running a 1-sample t-test (or 1-sample z-test if you go the Z-route) provides us with a test-statistic of -10.33 (the same for z as well) and corresponing p-value of less than .0001. With an established p-value of .05, we easily reject the null hypothesis since .0001 is way below this threshold.

In conclusion, we are saying that, assuming a random and representative sample was taken from a city 60 times providing us with a mean of 25C, the chance that this city's actual mean temperature is actually 23C and not 25C is less than 1 in 10,000 (or extremely unlikely). We should conclude the mean is not 23C and is closer to 25C.

The 95% confidence interval around our sample suggests the true city average temperature to be somewhere between 24.6 and 25.4C.