Question

The effectiveness of a new treatment was tested against the existing procedure for Alzheimer's patients. A study randomized 13 patients to the new treatment and 18 patients to the existing. After 3 years, all patients relapsed, and Alzheimer's symptoms re-occurred. The average time-to-relapse was X_bar1=18.6 months under the new treatment and X_bar_2=10.1 months under the existing procedure, with observed standard deviation s_1=3 and s_2=3.2.

To test the difference between the mean relapse time of the new treatment and the standard procedure with α=0.05 we could also [select all that apply]:

	Compute a 95% confidence interval for the difference of the mean time-to-relapse between both drugs and reject the null hypothesis if the interval does not include 0
	Compute a 90% confidence interval for the difference of the mean time-to-relapse between both drugs and reject the null hypothesis if the interval does not include 0
	Compute a 90% confidence intervals for the mean time-to-relapse for both drugs separately, and reject the null hypothesis if two intervals overlap
	Compute a 90% confidence intervals for the mean time-to-relapse for both drugs separately, and reject the null hypothesis if two intervals do not overlap

The effectiveness of a new treatment was tested against the existing procedure for Alzheimer's patients. A study randomized 13 patients to the new treatment and 18 patients to the existing. After 3 years, all patients relapsed, and Alzheimer's symptoms re-occurred. The average time-to-relapse was X_bar1=18.6 months under the new treatment and X_bar_2=10.1 months under the existing procedure, with observed standard deviation s_1=3 and s_2=3.2.

The critical value for a one-sided test corresponds to

	Z_alpha
	Z_alpha/2
	t_alpha/2 with df=13+18-2
	t_alpha with df=13+18-2
	- t_alpha with df=13+18-2
	t_alpha with df=delta

The effectiveness of a new treatment was tested against the existing procedure for Alzheimer's patients. A study randomized 13 patients to the new treatment and 18 patients to the existing. After 3 years, all patients relapsed, and Alzheimer's symptoms re-occurred. The average time-to-relapse was X_bar1=18.6 months under the new treatment and X_bar_2=10.1 months under the existing procedure, with observed standard deviation s_1=3 and s_2=3.2.

Which test should be used to compare the treatments?

	Two-sample test for population difference in means (with unequal variances)
	One-sample test for population mean
	Paired test for population mean difference
	Two-sample test for population difference in means (with equal variances)

The effectiveness of a new treatment was tested against the existing procedure for Alzheimer's patients. A study randomized 13 patients to the new treatment and 18 patients to the existing. After 3 years, all patients relapsed, and Alzheimer's symptoms re-occurred. The average time-to-relapse was X_bar1=18.6 months under the new treatment and X_bar_2=10.1 months under the existing procedure, with observed standard deviation s_1=3 and s_2=3.2.

Which of the data assumptions is NOT valid?

	Population variances are equal
	Populations (and samples) are independent
	Population variances are not equal
	Both populations are normal or both samples are large

Answer 1

Which of the data assumptions is NOT valid?

Ans:

Population variances are not equal.

(Note using the F-test, the variances of the two population are the same)