Question

Researchers conducted an experiment to test the effects of alcohol. Errors were recorded in a test of visual and motor skills for a treatment group of 21 people who drank ethanol and another group of 21 people given a placebo. The errors for the treatment group have a standard deviation of 2.40​, and the errors for the placebo group have a standard deviation of 0.83. Use a 0.05 significance level to test the claim that the treatment group has errors that vary significantly more than the errors of the placebo group. Assume that the two populations are normally distributed.

What are the null and alternative​ hypotheses?

A. Ho​: σ 1 2 ≠ σ 2 2
   H1​:σ 1 2= σ 2 2

B. Ho​: σ 1 2= σ 2 2
   H1: σ 1 2> σ 2 2

C. Ho​: σ 1 2= σ 2 2
H1​: σ 1 2< σ 2 2

D. Ho​: σ 1 2= σ 2 2

H1: σ 1 2≠

Identify the test statistic.

________________​

(Round to two decimal places as​ needed.)

Use technology to identify the​ P-value.

______________

​(Round to three decimal places as​ needed.)

What is the conclusion for this hypothesis​ test?

A. Fail to reject Ho. There is sufficient evidence to support the claim that the treatment group has errors that vary significantly more than the errors of the placebo group.

B. Reject Ho. There is insufficient evidence to support the claim that the treatment group has errors that vary significantly more than the errors of the placebo group.

C. Reject Ho. There is sufficient evidence to support the claim that the treatment group has errors that vary significantly more than the errors of the placebo group.

D. Fail to reject Ho. There is insufficient evidence to support the claim that the treatment group has errors that vary significantly more than the errors of the placebo group.

Answer 1

i am denoting the treatment group by sample 1 and the placebo group by sample 2.

given data are:-

a).hypothesis:-

(B)

b).the test statistic be:-

c).df₁ = = (21-1) = 20

df₂ = = (21-1) = 20

the p value = 0.000

[ in any blank cell of excel type =F.DIST.RT(8.36,20,20) ]

d).decision:-

Reject Ho. There is sufficient evidence to support the claim that the treatment group has errors that vary significantly more than the errors of the placebo group.(C)

[ p value = 0.000 < 0.05 (alpha)]

*** if you have any doubts about the problem please mention it in the comment box... if satisfied please LIKE.