1. ## Binomial theorom help.

Hi,
I have been working on this problem for so long and can not seem to get the right answer. If anyone could explain how I do this I would greatly appreciate it. Ive tried the binomial formula but I get the wrong answer being "0.109375".

Here is the question:
In fiscal year 1996, the U.S. Agency for International Development provided 238,300 metric tons of corn soy blend (CSB) for development programs and emergency relief in countries throughout the world. CSB is a highly nutritious, low-cost fortified food that is partially precooked and can be incorporated into different food preparations by the recipients. Loss of vitamin C as a result of the cooking process was a concern of the researchers. To test their concern they selected 8 preparations of a product called gruel and measured the vitamin C content before and after cooking. If cooking has no effect on the amount of vitamin C, the number of preparations, X, of gruel with a lower vitamin C after cooking will have a binomial distribution with p = 1/2. The agency decides to test the hypothesis of no difference in vitamin C content against the alternative that there is a loss in vitamin C content by counting the number of preparations of gruel with a lower Vitamin C content after cooking. What is the P-value of their test if 6 of the preparations had a lower vitamin C content after cooking?
NOTE: If cooking lowers vitamin C content, X should be "large".
NOTE: Assume that with sampling error, there are no differences = 0.

Thanks!

2. Originally Posted by googy
Hi,
I have been working on this problem for so long and can not seem to get the right answer. If anyone could explain how I do this I would greatly appreciate it. Ive tried the binomial formula but I get the wrong answer being "0.109375".

Here is the question:
In fiscal year 1996, the U.S. Agency for International Development provided 238,300 metric tons of corn soy blend (CSB) for development programs and emergency relief in countries throughout the world. CSB is a highly nutritious, low-cost fortified food that is partially precooked and can be incorporated into different food preparations by the recipients. Loss of vitamin C as a result of the cooking process was a concern of the researchers. To test their concern they selected 8 preparations of a product called gruel and measured the vitamin C content before and after cooking. If cooking has no effect on the amount of vitamin C, the number of preparations, X, of gruel with a lower vitamin C after cooking will have a binomial distribution with p = 1/2. The agency decides to test the hypothesis of no difference in vitamin C content against the alternative that there is a loss in vitamin C content by counting the number of preparations of gruel with a lower Vitamin C content after cooking. What is the P-value of their test if 6 of the preparations had a lower vitamin C content after cooking?
NOTE: If cooking lowers vitamin C content, X should be "large".
NOTE: Assume that with sampling error, there are no differences = 0.

Thanks!
The probability of $6$ or more preparations having lower vitamin C content after
cooking if cooking has no effect on vitamin C content is:

$P(N \ge 6) = P(N=6)+P(N=7)+P(N=8)=$ $\ \frac{8!}{6!2!}0.5^8+\frac{8!}{7!1!}0.5^8+\frac{8! }{8!0!}0.5^8=0.5^8[28+8+1]\approx 0.1445$

RonL