Question

# An educator claims that the average salary of substitute teachers in school districts in Allegheny County,...

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?

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.

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