Question

In this week's problem, I interviewed my cycling group to see how many have participated in a Triathlon. I hypothesized that the population mean number of people who participated is 4, and my random sample results were: 2,7,3,2,3,0,0. I am choosing to test this hypothesis at the 0.1 significance level.

Answer 1

Let denotes the population mean.

To test against

Here

sample mean

sample standard deviation

and sample size

The test statistic can be written as

which under H₀ follows a t distribution with n-1 df.

We reject H₀ at 0.1 level of significance if

Now,

The value of the test statistic =

and critical value

Since , so we fail to reject H₀ at 0.1 level of significance and we can conclude that the population mean is not significantly different from 4