# power of test random sample

• September 9th 2008, 05:25 PM
wik_chick88
power of test random sample
Mary’s cat Baskin requires food with an expected meat content of 80%. From past experience it is known that the meat content in cat food has a normal distribution with standard deviation 5%. Mary buys a crate of cat food for her beloved boy. Baskin decides that he will take a random sample of 10 tins of food, and that he will reject the whole crate if the average meat content (for the sample) is less than 75%. Determine the power of Baskin’s test if the expected meat content is actually 77%.
• September 9th 2008, 09:41 PM
mr fantastic
Quote:

Originally Posted by wik_chick88
Mary’s cat Baskin requires food with an expected meat content of 80%. From past experience it is known that the meat content in cat food has a normal distribution with standard deviation 5%. Mary buys a crate of cat food for her beloved boy. Baskin decides that he will take a random sample of 10 tins of food, and that he will reject the whole crate if the average meat content (for the sample) is less than 75%. Determine the power of Baskin’s test if the expected meat content is actually 77%.

The power of a statistical test is the probability that the test will reject a false null hypothesis (that it will not make a Type II error).

Where are you stuck?
• September 14th 2008, 04:06 PM
wik_chick88
i honestly have no idea where to start...i need something to start me off!
• September 14th 2008, 08:51 PM
mr fantastic
Quote:

Originally Posted by wik_chick88
i honestly have no idea where to start...i need something to start me off!

Let Y be the random variable percentage meat content.

Let $\bar{X}$ be the random variable average percentage meat content of the sample.

Y ~ Normal $(\mu_Y = 77, \, \sigma_Y = 5)$.

Therefore $\bar{X}$ ~ Normal $(\mu_{\bar{X}} = .... \, \, \sigma_{\bar{X}} = .... )$.

Power $= \Pr( \bar{X} < 75)$.