Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations.
H0: μ1 − μ2 ≥ 0
HA: μ1 − μ2 < 0
x−1x−1 = 222x−2x−2 = 253s1 = 32s2 = 26n1 = 12n2 = 12
a-1. Calculate the value of the hypothesis test statistic under the assumption that the population variances are equal.
Note: Negative value should be indicated by a minus sign. Round final answer to 3 decimal places.
a-2. Find the p-value.
multiple choice 1
0.01 p-value < 0.025
0.025 p-value < 0.05
0.05 p-value < 0.10
p-value 0.10
p-value < 0.01
a-3. Do you reject the null hypothesis at the 5% level?
multiple choice 2
Yes, since the p-value is greater than the significance level.
No, since the p-value is greater than the significance level.
Yes, since the p-value is less than the significance level.
No, since the p-value is less than the significance level.
a-4. Interpret the results at α = 0.05.
multiple choice 3
We cannot conclude that the population means differ.
We conclude that the population means differ.
We cannot conclude that population mean 1 is less than population mean 2.
We conclude that population mean 1 is less than population mean 2.
b-1. Calculate the value of the hypothesis test statistic under the assumption that the population variances are unknown and are not equal.
Note: Negative value should be indicated by a minus sign. Round final answer to 3 decimal places.
b-2. Find the p-value.
multiple choice 4
0.01 p-value < 0.025
0.025 p-value < 0.05
0.05 p-value < 0.10
p-value 0.10
p-value < 0.01
b-3. Do you reject the null hypothesis at the 5% level?
multiple choice 5
Yes, since the p-value is greater than the significance level.
Yes, since the p-value is less than the significance level.
No, since the p-value is less than the significance level.
No, since the p-value is greater than the significance level.
b-4. Interpret the results at α = 0.05.
multiple choice 6
We cannot conclude that the population means differ.
We conclude that the population means differ.
We cannot conclude that population mean 1 is less than population mean 2.
We conclude that population mean 1 is less than population mean 2.