# Calculate power in Statistics

• March 12th 2009, 04:50 AM
DINOCALC09
Calculate power in Statistics
A cigarette manufacteror claims that the mean nicotine content of its cigarettes is 15 mg with a standard deviation of 0.25 mg. A simple random sample of 45 cigarettes is tested to determine the mean nicotine content. Using the following information, answer the questions.

Ho: population mean = 1.5
Ha: population mean > 1.5

Reject Ho when sample mean > 1.85

A.) Calculate the power of the test against the alternative value, alternative population mean =1.95. Assume a normal distribution.

I know power is 1 - a Type II error (failing to reject a false hypothesis). However, do not know how to go about solving this.

B.) What is the probability that you would make a Type II error.
• March 12th 2009, 11:02 PM
mr fantastic
Quote:

Originally Posted by DINOCALC09
A cigarette manufacteror claims that the mean nicotine content of its cigarettes is 15 mg Mr F says: Strong cigarettes .... You'd only need to smoke 1 a day I imagine. Much healthier than if the content was 1.5 mg, say .....

with a standard deviation of 0.25 mg. A simple random sample of 45 cigarettes is tested to determine the mean nicotine content. Using the following information, answer the questions.

Ho: population mean = 1.5
Ha: population mean > 1.5

Reject Ho when sample mean > 1.85

A.) Calculate the power of the test against the alternative value, alternative population mean =1.95. Assume a normal distribution.

I know power is 1 - a Type II error (failing to reject a false hypothesis). However, do not know how to go about solving this.

B.) What is the probability that you would make a Type II error.
Power = Pr(Type I error) = $\Pr(\text{Reject} H_0 \, | \, \mu = 1.95) = \Pr(\overline{X} > 1.85 \, | \, \mu = 1.95)$.
Pr(Type II error) = $\Pr(\text{Accept} H_0 \, | \, \mu = 1.95) = \Pr(\overline{X} < 1.85 \, | \, \mu = 1.95)$.