   Chapter 8, Problem 9P Essentials of Statistics for the B...

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

Solutions

Chapter
Section Essentials of Statistics for the B...

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

A random simple is selected from a normal population with a mean of μ = 100 and a standard deviation of σ = 20. After a treatment is administered to the individuals in the sample, the sample mean is found to be M = 96.a. How large a sample is necessary for this sample mean to be statistically significant? Assume a two-tailed test with α = .05.b. If the sample mean were M = 98, what sample size would be needed to be significant for a two-tailed test with α = .05?

a.

To determine
How large the sample size should be so that sample mean is statistically significant.

Explanation

Given info:

Samples mean (M) is 96, population mean is 100, standard deviation is 20 and alpha level is 0.05.

Calculation:

The sample mean is statistically significant when calculated value is greater than the critical value. For calculating critical value alpha level is given as 0.05:

p=1α2=10.052=10.025=0.975

Now check the value of z-score in z table at 0.975 then the z-score is ±1.96. Calculated z-value with the given data is calculated as:

z=MμσM

Where σM is known as standard error and calculated as

σM=σn

Substitute the standard error in z-score then:

z=Mμσn

The z score is,

z=Mμσn<

b.

To determine
How large the sample size should be so that sample mean is statistically significant.

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