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Essentials of Statistics for the B...

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

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Section
BuyFindarrow_forward

Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

A sample of n = 4 individuals is selected from a population with a mean of μ = 40. A treatment is administered to the individuals in the sample and. after treatment, the sample has a mean of M = 44 and a variance of s2 = 16.

a. Is this sample sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with α = .05.

b. If all other factors are held constant and the sample size is increased to n = 16, is the sample sufficient to conclude that the treatment has a significant effect? Again, use a two-tailed test with α = .05.

a.

To determine

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

Explanation

Given info:

A sample of 4 individual is selected from a population with mean 40. The sample mean and variance are 44 and 16 respectively. The two-tailed hypothesis test using α=0.05 is performed.

Calculations:

The test hypothesis is given below:

Null Hypothesis:

H0:μ=40

Alternative Hypothesis:

H1:μ40

Degrees of freedom:

d.f=n1=41=3

Critical value:

For a two-tailed test with α=0.05 and df=3, the critical value (CV)  is obtained from the t-table as t=±3.182

Test statistic:

The t-statistic is,

t=Mμsm

Calculate sm using the formula:

b.

To determine

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

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