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Essentials of Statistics for the B...

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

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Chapter
Section
BuyFindarrow_forward

Essentials of Statistics for the B...

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

To evaluate the effect of a treatment, a sample is obtained from a population with a mean of μ = 30, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 31.3 with a standard deviation of s = 3.

a. If the sample consists of n = 16 individuals, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α = .05?

b. If the sample consists of n = 36 individuals, are the data sufficient to conclude that the treatment has a significant cited using a two-tailed test with α = .05?

c. Comparing your answer for parts a and b, how does the size of the sample influence the outcome of a hypothesis test?

a.

To determine

To find: Whether or not to conclude that the treatment has a significant effect for the given question using two-tailed test with α=0.05 and n=16.

Explanation

Given info:

A sample of 16 individual is selected from a population with mean 30. The samples mean, standard deviation is found to be 31.3 and 3 respectively. Two-tailed hypothesis test using α=0.05 is to be performed.

Calculations:

Step 1: Null Hypothesis is H0:μ=30 and Alternate Hypothesis is H1:μ30

Step 2: For a sample of n=16, the t-statistics will have (n1) degrees of freedom, i.e. df=15. For a two-tailed test with α=0.05 and df=15, the critical value (CV)  is obtained from the t-table as t=±2.131

Step 3: t-statistics can be calculated using formula:

t=Mμsm

Calculate sm using the formula:

sm=s2n=(3)216=0

b.

To determine

To Find: Whether or not to conclude that the treatment has a significant effect for the given question using two-tailed test with α=0.05 and n=36

c.

To determine

To State: The impact of sample size on the outcome of a hypothesis test.

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