You may need to use the appropriate appendix table or technology to answer this question.
Consider the following hypothesis test.
H0: μ1 − μ2 = 0
Ha: μ1 − μ2 ≠ 0
The following results are for two independent samples taken from the two populations.
Sample 1 | Sample 2 |
---|---|
n1 = 80 |
n2 = 70 |
x1 = 104 |
x2 = 106 |
σ1 = 8.2 |
σ2 = 7.4 |
(a)
What is the value of the test statistic? (Round your answer to two decimal places.)
(b)
What is the p-value? (Round your answer to four decimal places.)
SOLUTION:
From given data,
The following results are for two independent samples taken from the two populations.
Sample 1 | Sample 2 |
= 80 | = 70 |
= 104 | = 106 |
= 8.2 | = 7.4 |
The statistical software output for this problem is:
Two sample Z summary hypothesis test:
: Mean
of population 1 (Std. dev. = 8.2)
: Mean
of population 2 (Std. dev. = 7.4)
-
:
Difference between two means
Null hypothesis : H0 : -
=
0
Alternative hypothesis : Ha : -
0
(a) What is the value of the test statistic? (Round your answer to two decimal places.)
Test statistic
z = ( - ) / sqrt ( / + / )
z = (104 - 106 ) / sqrt (8.22 / 80 + 7.42 / 70)
z = -2 / 1.273886
z = -1.56
(b) What is the p-value? (Round your answer to four decimal places.)
p-value
p-value = P (z > -1.56 )
= 1 - P (z < -1.56 )
= 1 - 0.05938
= 0.94062
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