Recall the bottle filling problem we discussed in class: The amount of cola put

Question

Recall the bottle filling problem we discussed in class: The amount of cola put into 20 oz. bottles by a certain bottling machine follows a normal distribution. If the machine is calibrated correctly, thenmu= 20 oz. The standard deviation is known to be0.1. You are concerned that the machine is over-filling the bottles, so you take a simple random sample of sizen= 6 bottles.

a) State your null and alternative hypotheses

b) At a significance level of 0.05, for what values of the mean of the samplewill you reject the null hypothesis?

c) What is the probability that you make a Type I error?

d) What is the power of the test to correctly choose the alternativemu= 20.1?

Explanation / Answer

a)Null hypo = H0 = mu = 20

Alternative= H1 = mu not equal to 20

b) mu lying in confidence interval will not be rejected, otherwise it wil be

20-0.1*(1.96)/sqrt(6) < mu < 20+0.1*(1.96)/sqrt(6)

19.92< mu< 20.08

c) Probability of making a type 1 error = alpha = 5%

d) P( Z>= (20-20.1)/(0.1/sqrt(6)) = p(-2.45) = 0.9929

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