Hypotheses for a statistical test are given, followed by several possible confidence intervals for different samples....

Hypotheses for a statistical test are given, followed by several possible confidence intervals for different samples. In each case, use the confidence interval to state a conclusion of the test for that sample and give the significance level used.

Hypotheses: H₀ : μ₁ = μ₂ vs H_a : μ₁ ≠ μ₂. In addition, in each case for which the results are significant, state which group (1 or 2) has the larger mean.

95% confidence interval for μ₁ − μ₂ : 0.12 to 0.54

99% confidence interval for μ₁ − μ₂ : −2.1 to 5.4

90% confidence interval for μ₁ − μ₂ : − 10.8 to −3.7

Solutions

Expert Solution

a. In case of 95% confidence interval, it means that the hypothesized difference between the means of the two groups lies between 0.12 and 0.54 in 95% of the samples. In this case, since the hypothesized difference(₁ - ₂)is positive, therefore the mean of group 1 is greater than that of group 2. Significance level used = 95%. Alpha = 1-0.95 = 0.05

b. In case of 99% confidence interval, it means that the hypothesized difference between the means of the two groups lies between -2.1 and 5.4 in 99% of the samples. The result of this confidence interval is insignificant as the difference can be both positive and negative. Thus, we cannot conclude which mean is bigger. Significance level used = 99%. Alpha = 1-0.99 = 0.01

c. In case of 90% confidence interval, it means that the hypothesized difference between the means of the two groups lies between -10.8 and -3.7 in 90% of the samples. In this case, since the hypothesized difference(₁ - ₂)is negative, therefore the mean of group 2 is greater than that of group 1. Significance level used = 90%. Alpha = 1-0.9 = 0.1

orchestra answered 1 year ago

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