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 25 people who drank ethanol and another group of 25 people given a placebo. The errors for the treatment group have a standard deviation of 2.60, and the errors for the placebo group have a standard deviation of 0.68. 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. Upper H 0H0​:
sigma Subscript 1 Superscript 2σ21equals=sigma Subscript 2 Superscript 2σ22
Upper H 1H1​:
sigma Subscript 1 Superscript 2σ21not equals≠sigma Subscript 2 Superscript 2σ22
B. Upper H 0H0​:
sigma Subscript 1 Superscript 2σ21equals=sigma Subscript 2 Superscript 2σ22
Upper H 1H1​:
sigma Subscript 1 Superscript 2σ21greater than>sigma Subscript 2 Superscript 2σ22
C. Upper H 0H0​:
sigma Subscript 1 Superscript 2σ21not equals≠sigma Subscript 2 Superscript 2σ22
Upper H 1H1​:
sigma Subscript 1 Superscript 2σ21equals=sigma Subscript 2 Superscript 2σ22
D. Upper H 0H0​:
sigma Subscript 1 Superscript 2σ21equals=sigma Subscript 2 Superscript 2σ22
Upper H 1H1​:
sigma Subscript 1 Superscript 2σ21less than Identify the test statistic.
nothing
​(Round to two decimal places as​ needed.)

Answer 1

H0: σ1=σ2

Ha : σ1 >σ2

B. Upper H 0H0​:

sigma Subscript 1 Superscript 2σ21equals=sigma Subscript 2 Superscript 2σ22

Upper H 1H1​:

sigma Subscript 1 Superscript 2σ21greater than>sigma Subscript 2 Superscript 2σ22

Explanation:

The claim is that the treatment group has errors that vary significantly more than the errors of the placebo group.

The claim is the alternative hypothesis and the opposite of claim is the null hypothesis.

Vary significantly means that it is greater than so we choose the alternate hypothesis of greater than and the null hypothesis will be equal to errors of the placebo group.

So the correct choice is B.

B. Upper H 0H0​:

sigma Subscript 1 Superscript 2σ21equals=sigma Subscript 2 Superscript 2σ22

Upper H 1H1​:

sigma Subscript 1 Superscript 2σ21greater than>sigma Subscript 2 Superscript 2σ22

Choice A,C and D all are incorrect.

This can be written as

H0: σ1=σ2

Ha : σ1 >σ2