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1) Statisticians always prefer larger samples sizes to small ones. Describe the effect of increasing the size of a sample (the number of participants in an experiment) from 25 to 100 on the following, assuming the mean and standard deviations of the samples remain constant: (6 pts) a. How would the margin of error of a 95% confidence interval change

User RolandJS
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1 Answer

5 votes

Answer:

The margin of error reduces to half of it original size

Explanation:

From the question we are told the confidence level is 95% , hence the level of significance is


\alpha = (100 - 95 ) \%

=>
\alpha = 0.05

Generally from the normal distribution table the critical value of
(\alpha )/(2) is


Z_{(\alpha )/(2) } =  1.96

Generally the margin of error is mathematically represented as


E = Z_{(\alpha )/(2) } *  (\sigma )/(√(n) )

Let assume the standard deviation is
\sigma = 0.4

When sample size is n = 25


E = 1.96 *  (0.4 )/(√(25) )


E =0.1568

When sample size is n = 100


E_1 = 1.96 *  (0.4 )/(√(100) )


E_1 = 0.0784

So


(E_1)/(E) = (0.0784)/(0.1568) = (1)/(2)

Hence the margin of error reduces to half of it original size

User XssChauhan
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