Question

1. If two samples are drawn independently from the same population, then the sample means will be the same.

true or false?

2. If two samples are drawn independently from the same population, then their sample standard deviations will be the same.

true or false?

3. You can find below the results from Tukey's Honestly Significant Difference procedure with familywise significance level 0.05 for the agricultural experiment above. Which of the following can be concluded at this level?

	diff	lwr	upr	p adj
B-A	7.649	-11.133	26.431	0.719
C-A	16.443	-2.339	35.225	0.101
D-A	3.916	-14.866	22.698	0.965
E-A	27.331	8.549	46.114	0.003
C-B	8.794	-9.989	27.576	0.610
D-B	-3.733	-22.516	15.049	0.971
E-B	19.682	0.900	38.464	0.038
D-C	-12.527	-31.309	6.255	0.287
E-C	10.888	-7.894	29.671	0.414
E-D	23.416	4.633	42.198	0.012

Group of answer choices:

Group B has higher average output than group A

Groups E and C have higher average output than groups A, B, and D

Group E has higher average output than groups A, B, C, and D

Group E has higher average output than groups A, B, and D

Group A has lower average output than groups B, C, D, and E

Answer 1

(1)

Correct option:

False

Explantion:

If two samples are drawn independently from the same population, then the sample means will be different because of random errors in sampling.

(2)

Correct option:

False

Explantion:

If two samples are drawn independently from the same population, then their sample standard deviations will be different because of random errors in sampling.

(3)

Correct option:

Group E has higher average output than groups A, B, and D

Explanation:

(i)

Group B has higher average output than group A is not correct because the Confidence Interval for B - A: ( - 11.133, 26.431) includes 0.

(ii)

Groups E and C have higher average output than groups A, B, and D is not correct because the Confidence Interval for C - B: ( -9.989, 27.576) includes 0.

(iii)

Group E has higher average output than groups A, B, C, and D is not correct because the Confidence Interval for E - C: ( -7.894, 29.671) includes 0.

(iv)

Group E has higher average output than groups A, B, and D is correct because the Confidence Interval for E - A, E - B and E - D do not include 0.

(v)

Group A has lower average output than groups B, C, D, and E is not correct because the Confidence Interval for B - A: ( - 11.133, 26.431) includes 0.