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)
H0: μ1 − μ2 = 0
HA: μ1 − μ2 ≠ 0
x̄1 = 68
x̄2 = 80
σ1 = 12.30
σ2 = 1.68
n1 = 15
n2 = 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 ≥ 0.10
0.05 ≤ p-value < 0.10
0.025 ≤ p-value < 0.05
0.01 ≤ p-value < 0.025
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 α = 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.