Question

A certain medication is supposed to contain 350 mg of the active ingredient per pill. It is known from previous work that this content is normally distributed with a standard deviation of 3.5 mg. Suppose a random sample of 5 pills are taken, and the average content is 346.4 mg. Is the mean pill content not 350 mg?

a) For this example, if we were to test our hypothesis at the level a= 0.01 what would our conclusion be ?

b) What would our conclusion be at the level a = 0.05 ?

Answer 1

H0: = 350

Ha: 350

Test statistics

z = - / / sqrt(n)

= 346 - 350 / 3.5 / sqrt(5)

= -2.56

p-value = 2 * P( Z < z)

= 2 * P( Z < -2.56)

= 2 * 0.0052

= 0.0104

a)

At 0.01 significance level,

Since p-value > 0.01 level, do not reject H0.

b)

At 0.05 significance level,

Since p-value < 0.05 level, Reject H0.