Question

a. We are testing H₀: μ₁ - μ₂ = 0. Our 95% confidence interval is (-27.01,-7.5).
We should expect the t-statistic to be  ---Select--- greater than 2 between 0 and 2 between 0 and -2 less than -2 .
We should expect the p-value to be  ---Select--- less than .05 greater than .05 equal to .05 .
We should  ---Select--- reject fail to reject H₀ and conclude that the group 1 population average is  ---Select--- smaller larger than the group 2 population average.
It is possible that we could be making a  ---Select--- Type I Type II error.

b. We are testing H₀: μ = 15. Our t statistic is 1.25.
We can tell that in our sample, the sample average was  ---Select--- greater less than 15.
We should expect the 95% confidence interval to  ---Select--- include exclude 15.
We should expect the p-value to be  ---Select--- less than .05 greater than .05 equal to .05 .
We should  ---Select--- reject fail to reject H₀.
It is possible that we could be making a  ---Select--- Type I Type II error.

Answer 1

Solution:

a. We are testing H₀: μ₁ - μ₂ = 0. Our 95% confidence interval is (-27.01,-7.5).
We should expect the t-statistic to be less than -2. (Because the confidence interval contains all the negative values)
We should expect the p-value to be less than .05. (Since the confidence interval is significant at 0.05 significance level, therefore, the p-value is expected to be less than 0.05)
We should reject H₀ and conclude that the group 1 population average is smaller larger than the group 2 population average. (Since the confidence interval contains the negative values, therefore, the group 1 population average is smaller than the group 2 population average)
It is possible that we could be making a Type I. (Type I error is the error of rejecting the null hypothesis, when, in fact it is true)

b. We are testing H₀: μ = 15. Our t statistic is 1.25.
We can tell that in our sample, the sample average was greater than 15. (Since the test statistic is positive, it means, the sample mean will be greater than 15)
We should expect the 95% confidence interval to include15. ( Since the test statistic is less than the 2 standard deviations above the mean, we, therefore can expect to see 15 included in the confidence interval)
We should expect the p-value to be greater than .05. (The p-value is expected to be greater than 0.05)
We should fail to reject H₀. (Since the p-value is expected to be greater than 0.05, we, therefore, fail to reject the H0)
It is possible that we could be making a Type II error. (Type II error is the error failing to reject the null hypothesis, when H0 is in fact false)