age of college students

Question

Find the 90% confidence interval for the variance and standard deviation of the ages of seniors at oak park college if a sample of 22 students has a variance of 2.6 years. assume the variable is normally distributed

Answer 1

This one will require you to use the chi-square table in order for you to find the confidence interval for variance and standard deviation.

n = 22 students and s² = 2.6 years

DF (degrees of freedom) = 22 - 1 = 21 and α = 0.10 (10% level of significance)

By using the chi-square table, you should get χ²_0.05 = 32.671 and χ²_0.95 = 11.591.

Use the following inequality to find the confidence interval for variance and standard deviation:

[(n - 1)*s²] / χ²_0.05 ≤ σ² ≤ [(n - 1)*s²] / χ²_0.95

[(22 - 1)*(2.6)] / 32.671 ≤ σ² ≤ [(22 - 1)*(2.6)] / 11.591

1.671 ≤ σ² ≤ 4.711 (Confidence Interval for Variance)

1.293 ≤ σ ≤ 2.170 (Confidence Interval for Standard Deviation)