Posted by **Allan** on Sunday, March 14, 2010 at 9:31am.

The diameter of a wire should be 8 cm. It follows a normal distribution and has a standard deviation of 0.01 cm.

A person tests each delivery by taking 5 samples, accepting the goods only if the mean is at most 8.01

a)

Find the probability of type 1 error?

b)

A hypothesis test is to be carried out with P(type I error) = P(type II error) and either one being at 0.1%.

What is the necessary sample size for this test? (answer in my book says it's n=17)

2)

A company will sell a new product if the proportion of customers that will buy it is at least 20%. It is decided that the null hypothesis is rejected if the sample proportion is at least 27%. Sample size = 100.

a) Find P(type I error)

b)

If P(do not reject the null hypothesis)must be at least 99% if the true proportion is 0.17 and

P(reject the null hypothesis)must be at least 99% if the true proportion is 0.27:

which sample size is required?

(My book's answer is n = or greater than 365)

I don't understand how to solve these kind of questions, I'd greatly appreciate if you could help explain !

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