Question

A random sample of 25 bottles of buffered aspirin contain, on average, 325.5 mg of aspirin with a sample standard deviation of 0.5 mg.

(a) Find a 95% two-sided confidence interval on the mean aspirin in milligram

(b) Construct a two-sided tolerance interval on the mean aspirin required that has confidence level 95% with 99% probability of coverage.

(c) Construct a two-sided 95% prediction interval on the amount of aspirin of the 26th sample.

Answer 1

Answer:

a)

degree of freedom = n - 1 = 25 - 1 = 24

alpha = 0.05

t(alpha/2 , df) = 2.063899 = 2.064

95% CI = xbar +/- t*s/sqrt(n)

substitute values

= 325.5 +/- 2.064*0.5/sqrt(25)

= 325.5 +/- 0.2064

= (325.294 , 325.706)

b)

k = sqrt((n-1)(1+1/n)*z/)

substitute values

= sqrt(24*(1+1/25)*1.645/13.85)

= 1.722

CI = xbar +/- k*s

substitute values

= 325.5 +/- 1.722*0.5

= (324.64 , 326.36)

c)

Prediction interval = xbar +/- t*s*sqrt(1 + 1/n)

substitute values

= 325.5 +/- 2.064*0.5*sqrt(1 + 1/25)

= 325.5 +/- 1.0524

= (324.45 , 326.55)