Question

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

Answer 1

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