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A sample of n = 16 individuals is selected from a population with a mean of μ = 80. A treatment is administered to the sample and. after treatment, the sample mean is found to be M = 86 with a standard deviation of s = 8. a. Does the sample provide sufficient evidence to conclude that the treatment has a significant effect? Test with α = .05. b. Compute Cohen's d and r 2 to measure the effect size. с. Find the 95% confidence interval for the population mean after treatment.

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Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
Publisher: Cengage Learning
ISBN: 9781133956570
BuyFind

Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
Publisher: Cengage Learning
ISBN: 9781133956570

Solutions

Chapter
Section
Chapter 9.3, Problem 1LCA
Textbook Problem

A sample of n = 16 individuals is selected from a population with a mean of μ = 80. A treatment is administered to the sample and. after treatment, the sample mean is found to be M = 86 with a standard deviation of s = 8.

a. Does the sample provide sufficient evidence to conclude that the treatment has a significant effect? Test with α = .05.

b. Compute Cohen's d and r2 to measure the effect size.

с. Find the 95% confidence interval for the population mean after treatment.

Expert Solution

a.

To determine

To test: Whether there is sufficient evidence to infer that the treatment has significant effect.

Explanation of Solution

Given info:

A sample of 16 individual is selected from a population with mean 80. The sample mean, and standard deviation (s) are 86 and 8 respectively. One-tailed hypothesis test using α=0.05 is to be performed.

Calculations:

Test hypothesis is given below:

Null Hypothesis:

H0:μ80

Alternative Hypothesis:

H1:μ>80

Degrees of freedom:

d.f=n1=161=15

Critical value:

For a one-tailed test with α=0.05 and df=15, the critical value (CV)  is obtained from the t-table as t=±2.131.

Test statistic:

The t-statistics is,

t=Mμsm

Calculate sm using the formula:

sm=sn

Expert Solution

b.

To determine

To find: The Cohen’s d and r2 to measure the effect size.

Expert Solution

c.

To determine

To construct: The 95% confidence interval for the population mean.

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