We wish to conduct a test of hypothesis on two independent population means. The alternative hypothesis of the test states that the means differ. Both populations are assumed normal with equal variance. We draw 10 observations for the first sample and 20 observations for the second sample. State the decision rule for the test if the level of significance is 0.01.Question 2Select one:a.we reject Ho if t > 2.4671b.we reject Ho if t <-2.4671 or t > 2.4671c.we reject Ho if t > 2.3263d.we reject Ho if t <-2.7633 or t > 2.7633
Question
We wish to conduct a test of hypothesis on two independent population means. The alternative hypothesis of the test states that the means differ. Both populations are assumed normal with equal variance. We draw 10 observations for the first sample and 20 observations for the second sample. State the decision rule for the test if the level of significance is 0.01.Question 2Select one:a.we reject Ho if t > 2.4671b.we reject Ho if t <-2.4671 or t > 2.4671c.we reject Ho if t > 2.3263d.we reject Ho if t <-2.7633 or t > 2.7633
Solution
The decision rule for the test, given a level of significance of 0.01, is based on the t-distribution. Since the alternative hypothesis states that the means differ, we are conducting a two-tailed test.
The degrees of freedom for this test are calculated by adding the number of observations from both samples and subtracting 2 (10 + 20 - 2 = 28).
Looking up the t-value for a two-tailed test with a significance level of 0.01 and 28 degrees of freedom in a t-distribution table, we find the critical value to be approximately 2.7633.
Therefore, the correct decision rule is:
d. We reject Ho if t < -2.7633 or t > 2.7633.
This means that if our calculated t-value is less than -2.7633 or greater than 2.7633, we reject the null hypothesis (Ho) and conclude that there is a significant difference between the two population means. If the calculated t-value falls within this range, we do not reject the null hypothesis and conclude that there is not a significant difference between the two population means.
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