Question

An educator claims that the average salary of substitute teachers in school districts in NC earn less than $82 per day. A random sample of twelve districts is selected, and the daily salaries are given below. With α = 0.10, is there enough evidence to support the claim? Please show all steps.

89 75 90 77 60 100 75 85 80 100 75 85

Identify the Null Hypothesis:

Identify the Alternate Hypothesis:

Work: Please show formula

Answer 1

Let denotes the average salary of substitute teachers in school districts in NC earn.

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 10% level of significance if

Now,

The value of the test statistic

and critical value

Since , so we fail to reject H₀ at 10% level of significance and we can conclude that the average salary of substitute teachers in school districts in NC earn is not significantly less than $82 per day.