The following table shows the average hourly wage rates for? day-care centers fr
ID: 3368736 • Letter: T
Question
The following table shows the average hourly wage rates for? day-care centers from two locations based on two random samples. Use the table to complete parts a through c.
Location 1
Location 2
Sample mean
?$9.549.54
?$8.528.52
Sample standard deviation
?$1.241.24
?$1.181.18
Sample size
2121
3131
a. Perform a hypothesis? test, using
alpha?equals=0.100.10?,
to determine if the average hourly wage for? day-care workers in Location 1 is? $0.50 per hour higher than the average hourly wage for? day-care workers in Location 2. Assume the population variances for wage rates in each location are equal.
Determine the null and alternative hypotheses for the test.
Upper H 0 : mu 1 minus mu 2H0: ?1??2
?
not equals?
less than<
equals=
greater than or equals?
greater than>
less than or equals?
?$0.50Upper H 1 : mu 1 minus mu 2H1: ?1??2
?
greater than>
less than or equals?
not equals?
less than<
greater than or equals?
equals=
?$0.50
Location 1
Location 2
Sample mean
?$9.549.54
?$8.528.52
Sample standard deviation
?$1.241.24
?$1.181.18
Sample size
2121
3131
Explanation / Answer
a)
H0 : nu1 - mu2 = 0.5
Ha : mu1 - mu2 > 0.5
b)
Test statistics:
t = ( x1 - x2)/sqrt(s1^2/n1 + s2^2/n2)
= ((9.54 - 8.52)- 0.5)/sqrt(1.24 ^2/21 + 1.18^2/31)
= 1.5129
p value = .0729
we reject the null hypothesis.
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