# college

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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 !

• probability and statistics) - ,

Help wanted in this subject