Question

The Allegheny County, Pennsylvania school district states that the average salary of substitute teachers in school districts in Allegheny County, Pennsylvania, is $60 per day. A disgruntled teacher believes the salary is actually less than this amount. A random sample of five school districts is selected, and the daily salaries (in dollars) are shown. Based on the evidence below, does it look like the disgruntled teacher is correct? Note: In your summary statement, remember to comment on the italicized phrase. You can use α = .10.

60 56 60 55 70

Part A: Solve for ?̅ :

Part B: Solve for s:

Part C: State ho and h1:

Part D: Solve for Critical Values t α/2:

Part E: Calculate

Part F: Apply Decision Rule to determine if ho should be accepted or rejected:

Part G: Summary Statement:

Answer 1

Part A Mean

Now for standard deviation s

Create the following table.

data	data-mean	(data - mean)2
60	-0.2	0.040000000000001
56	-4.2	17.64
60	-0.2	0.040000000000001
55	-5.2	27.04
70	9.8	96.04

Find the sum of numbers in the last column to get.

Part C Now and

Part D

The t-critical value for a left-tailed test, for a significance level of α=0.10 is

tc​=−1.533

Graphically

Part E t-value

Part F:As t value is not in the rejection area we fail to reject the null hypothesis.

Part G: We do not have sufficient evidence to support the claim.