Consider the following competing hypotheses and accompanying
sample data drawn independently from normally distributed
populations. (You may find it useful to reference the
appropriate table: z table or t
table)
H_{0}: μ_{1} −
μ_{2} = 0
H_{A}: μ_{1} −
μ_{2} ≠ 0
x−1x−1 = 68 | x−2x−2 = 80 |
σ_{1} = 12.30 | σ_{2} = 1.68 |
n_{1} = 15 | n_{2} = 15 |
a-1. Calculate the value of the test statistic.
(Negative values should be indicated by a minus sign. Round
all intermediate calculations to at least 4 decimal places and
final answer to 2 decimal places.)
a-2. Find the p-value.
p-value < 0.01
a-3. Do you reject the null hypothesis at the 5%
significance level?
No, since the p-value is more than α.
No, since the p-value is less than α.
Yes, since the p-value is more than α.
Yes, since the p-value is less than α.
a-4. Interpret the results at αα = 0.05.
We cannot conclude that the population means differ.
We conclude that the population means differ.
We cannot conclude that population mean 2 is greater than population mean 1.
We conclude that population mean 2 is greater than population mean 1.
The statistical software output for this problem is :
Test statistics = -3.74
p-value < 0.01
Yes, since the p-value is less than α.
e conclude that the population means differ.
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