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What sample size should be used if we would like to estimate the mean age of the college students at a particular campus with 95% confidence? We would like to be accurate to within three years, and we will assume the population is normally distributed with a standard deviation of 5.1 years.

Answer :

JeanaShupp

Answer: 12

Step-by-step explanation:

The formula to find the sample size is given by:-

[tex]n=(\dfrac{z_c\cdot \sigma}{E})^2[/tex] , where [tex]\sigma[/tex] is the population standard deviation, [tex]z_c[/tex] is the z-value for the [tex](1-\alpha)[/tex] confidence interval and E is the margin of error .

As per given , we have

Population standard deviation : [tex]\sigma=5.1[/tex]

z-value for 95% confidence interval : [tex]z_c=1.960[/tex]

Margin of error : E= 3

Then, the required minimum sample :-

[tex]n=(\dfrac{(1.96)\cdot (5.1)}{3})^2\\\\\Rightarrow\ n=(3.332)^2=11.102224\approx12[/tex]

Hence, the required minimum sample size = 12

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