Question

An educator claims that the average salary of substitute teachers in school districts in Allegheny County, Pennsylvania is less than $65 per day. A random sample of eight schools districts is selected and the daily salaries are shown below. Is there enough evidence to support the educator’s claim? Perform the appropriate hypothesis test using a significance value of 0.05.

.

              65         68         64         63         65         59         63              58

Find the p-value for the above hypothesis test.

What do you conclude using the p-value?

Answer 1

Calculating the sample mean, sample standard deviation for the given sample, we get
= 63.125 , 3.27 , n=8

For the given problem,

Null hypothesis:

Alternate hypothesis:

Since we have unknown population standard deviation and the sample size is less than 30, we use the one sample t test.

Substituting the values   = 63.125 , 3.27 , n=8   we get

t = -1.6215

For df of 7 (n-1), significance value of 0.05 and considering left tailed t test, we get a t critical value or p value of -1.895.

Since the calculated value of t (-1.6215) is greater than the p value (-.1.895), we cannot reject the null hypothesis.