Question

You may need to use the appropriate technology to answer this question.

A production line operation is tested for filling weight accuracy using the following hypotheses.

Hypothesis	Conclusion and Action
H0: μ = 16	Filling okay; keep running.
Ha: μ ≠ 16	Filling off standard; stop and adjust machine.

The sample size is 30 and the population standard deviation is σ = 0.7 Use α = 0.05.

What is the probability of making a type II error when the machine is overfilling by 0.4 ounces? (Round your answer to four decimal places.)

What is the power of the statistical test when the machine is overfilling by 0.4 ounces? (Round your answer to four decimal places.)

Answer 1

given data are:-

sample size(n) = 30

= 0.05

= 0.7

hypothesis:-

type II error :-

it is defined as fail to reject the null hypothesis, when it is false.

a). z critical value for 95% confidence level, both tiled test be-

the mean increased by the product of z score and sd be:-

now we have to calculate the probability of making a type II error when the machine is overfilling by 0.4 ounces.

the needed z scores be:-

the probability of making a type II error when the machine is overfilling by 0.4 ounces be:-

[ from standard normal table]

b). the power of the statistical test when the machine is overfilling by 0.4 ounces be:-

= 1- P(type II error)

= 1-0.1210

= 0.8790

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