BASIC PRACTICE OF STATISTICS+LAUNCHPAD
BASIC PRACTICE OF STATISTICS+LAUNCHPAD
8th Edition
ISBN: 9781319053093
Author: Moore
Publisher: MAC HIGHER
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Chapter 21, Problem 21.26E

(a)

To determine

To find: The two sample standard deviations.

(a)

Expert Solution
Check Mark

Answer to Problem 21.26E

The two sample standard deviations are 0.25 and 0.15.

Explanation of Solution

Given info:

In the given information, nAlcohol=25 , nPlacebo=25 , x¯Alcohol=0.25 , x¯Placebo=0.12 , SEMAlcohol=0.05 , and SEMPlacebo=0.03 .

Calculation:

The sample standard deviation for alcohol is,

SEMAlcohol=sAlcoholnAlcoholsAlcohol=SEMAlcoholnAlcohol=0.05(25)=0.25

The sample standard deviation for placebo is,

SEMPlacebo=sPlacebonPlacebosPlacebo=SEMPlacebonPlacebo=0.03(25)=0.15

Thus, the two sample standard deviations are 0.25 and 0.15.

(b)

To determine

To find: The degrees of freedom by using conservative Option 2 for two-sample t procedures.

(b)

Expert Solution
Check Mark

Answer to Problem 21.26E

The degrees of freedom are 24.

Explanation of Solution

Calculation:

The degrees of freedom for the two-sample t procedures with the conservative Option 2 is,

df=Smaller of nAlcohol1 and nPlacebo1=251=24

Thus, the degrees of freedom are 24.

(c)

To determine

To find: The 90% confidence interval for the mean difference between the two groups.

(c)

Expert Solution
Check Mark

Answer to Problem 21.26E

The 90% confidence interval for the mean difference between the two groups is (0.0302,0.2298) .

Explanation of Solution

Calculation:

Critical value:

From the table of “t Distribution critical values”, the critical value for 24 degrees of freedom with 90% confidence level is 1.711.

Confidence interval:

The 90% confidence interval for the mean difference between the two groups is,

CI=(x¯Alcoholx¯Placebo)±t*sAlcohol2nAlcohol+sPlacebo2nPlacebo=(x¯Alcoholx¯Placebo)±t*SEMAlcohol2+SEMPlacebo2=0.250.12±1.7110.052+0.032=0.13±0.0998

=(0.130.0998,0.13+0.0998)=(0.0302,0.2298)

Thus, the 90% confidence interval for the mean difference between the two groups is (0.0302,0.2298) .

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