An employment information service claims the mean annual salary for full-time female workers over age 25 and without a high school diploma is $18,500. The annual salaries for a random sample of 12 full-time female workers without a high school diploma are shown below.
Salaries |
|||||
19,665 |
21,354 |
20,177 |
19,794 |
19,316 |
22,445 |
21,864 |
17,312 |
20,143 |
18,328 |
20,403 |
20,237 |
Instructions: Round all your math steps to two decimal places just like I have been doing in class.
a. Compute the value of the test statistic. (Round to two decimal places) Answer
b. At α=0.05, test the claim that the mean salary is more than $18,500. What is your conclusion? Answer
a)
H0 : mu = 18500
Ha: mu > 18500
from the given data,
xbar =20086.50
s = 1417.74
t = (xbar - mu)/(sigma/sqrt(n))
= ( 20086.50- 18500)/(1417.74/sqrt(12))
= 3.88
p value = 0.0013
b)
Reject H0 as p value < 0.05
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