nsider 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)
Consider the following competing hypotheses and accompanying sample data drawn independently from
H0: μ1 − μ2 ≥ 0
HA: μ1 − μ2 < 0
|
x⎯⎯1x¯1
= 249 |
x−2x−2
= 262 |
| s1 = 35 | s2 = 23 |
| n1 = 10 | n2 = 10 |
a-1. Calculate the value of the test statistic under the assumption that the population variances are equal. (Negative values should be indicated by a minus sign. Round all intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)
a-2. Find the p-value.
multiple choice 1
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p-value < 0.01
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0.01 ≤ p-value < 0.025
-
0.025 ≤ p-value < 0.05
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0.05 ≤ p-value < 0.10
-
p-value ≥ 0.10
a-3. Do you reject the null hypothesis at the 5% level?
multiple choice 2
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Yes, since the value of the p-value is less than the significance level.
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No, since the value of the p-value is less than the significance level.
-
Yes, since the value of the p-value is greater than the significance level.
-
No, since the value of the p-value is greater than the significance level.
a-4. Interpret the results at
= 0.05.
multiple choice 3
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We conclude that the population means differ.
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We cannot conclude that the population means differ.
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We conclude that population mean 1 is less than population mean 2.
-
We cannot conclude that population mean 1 is less than population mean 2.
b-1. Calculate the value of the test statistic under the assumption that the population variances are not equal. (Negative values should be indicated by a minus sign. Round all intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)
b-2. Find the p-value.
multiple choice 4
-
p-value < 0.01
-
0.01 ≤ p-value < 0.025
-
0.025 ≤ p-value < 0.05
-
0.05 ≤ p-value < 0.10
-
p-value ≥ 0.10
b-3. Do you reject the null hypothesis at the 5% level?
multiple choice 5
-
Yes, since the value of the p-value is less than the significance level.
-
No, since the value of the p-value is less than the significance level.
-
Yes, since the value of the p-value is greater than the significance level.
-
No, since the value of the p-value is greater than the significance level.
b-4. Interpret the results at
= 0.05.
multiple choice 6
-
We conclude that the population means differ.
-
We cannot conclude that the population means differ.
-
We conclude that population mean 1 is less than population mean 2.
-
We cannot conclude that population mean 1 is less than population mean 2
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