Respuesta :
Answer:
99% confidence requires 243 subjects
95% confidence requires 118 subjects
The decrease in confidence makes the sample size smaller.
Step-by-step explanation:
The sample size n in Simple Random Sampling is given by
[tex]\bf n=\frac{z^2s^2}{e^2}[/tex]
where
z = 2.807 is the critical value for a 99% confidence level (*)
s = 11.1 is the estimated population standard deviation
e = 2 points is the margin of error
so
[tex]\bf n=\frac{z^2s^2}{e^2}=\frac{(2.807)^2(11.1)^2}{(2)^2}=242.7\approx 243[/tex]
(*)This is a point z such that the area under the Normal curve N(0,1) outside the interval [-z, z] equals 1% = 0.001
It can be obtained in Excel with
=NORMINV(1-0.0025,0,1)
and in OpenOffice Calc with
=NORMINV(1-0.0025;0;1)
A 95% confidence level would only change the value of z, which now would be 1.96, and the sample size changes to
[tex]\bf n=\frac{z^2s^2}{e^2}=\frac{(1.96)^2(11.1)^2}{(2)^2}=118.33\approx 118[/tex]
The decrease in confidence makes the sample size smaller.
The decrease in confidence level affected the sample size as it led to a reduction in the sample size.
What is a sample size?
A sample size simply means a term that's used to define the number of subjects that are included in a sample size.
At 99% confidence level, the number of subjects will be:
= [(2.58 × 11.1)/2]²
= 14.319²
= 205
At 95% confidence level, the number of samples will be:
= [(1.96 × 11.1)/2]²
= 119
In conclusion, the decrease in confidence affected the sample size as it led to a reduction in the sample size.
Learn more about sample size on:
https://brainly.com/question/25574075
