The ages of a group of 135 randomly selected adult females have a standard deviation of 18.3 years. Assume that the ages of female statistics students have less variation than ages of females in the general population, so let sigmaequals18.3 years for the sample size calculation. How many female statistics student ages must be obtained in order to estimate the mean age of all female statistics students? Assume that we want 90% confidence that the sample mean is within one-half year of the population mean.

The number of female statistics student ages that must be obtained in order to estimate the mean age of all female statistics students is; 3625 students ages.

We are given;

Standard deviation; σ = 18.3

Margin of error; E = 1/2 year

Confidence level; CL = 90%

Now, formula for margin of error is;

E = z(σ/√n)

Where;

E is margin of error

z is critical value at confidence level

σ is standard deviation

n is required sample size

The critical value of z at CL of 90% is;

z = 1.645

Let's make n the subject of the formula to get;

n = (zσ/E)²

n = (1.645 × 18.3/½)²

n = 3,624.882849

Approximating to a whole number gives;

n = 3625 females

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Therefore, the number of female statistics student ages that must be obtained in order to estimate the mean age of all female statistics student is 3625 female statistics student

Step-by-step explanation:

Here, we have

Where:

n = Required sample size

σ = Standard deviation = 18.3

E = Margin of error = 1/2 year

= Critical score from the confidence level = 1.645

Therefore,

Therefore, the number of female statistics student ages that must be obtained in order to estimate the mean age of all female statistics student = 3625 female statistics student.