Statistics problem

hockeyplayer42

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May 10, 2010
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(a)Let Y have a binomial distribution with parameters n and p. We reject Ho: p=1/2 and accept H1: p>1/2 if Y>=c. Find n and c such that the probability of a Type I error is .10, and P(reject Ho/p=2/3)=.95.
(b)What is the probability of a Type II error?


I dont know how to solve for n and c, but the confidence must be .9 since error 1 is .10. I dont know what to do next. I believe Beta is .1 and mu is 1/2 and by creating a normal distribution graph i think the critical value is 1.28. I am not sure how to come up with n or c.


Let X1,...,X9 be a random sample of size 9 from a distribution that is N(mu,sigma squared). If sigma is known, find the length of a 95% confidence interval for mu if this interval is based on the random variable Squarert9(xbar-mu)/sigma.


So confidence is obviously 95%, so do i SquarRt9(xbar-mu/sigma)=.95? I dont know what i do with N=9 I figured the formula would be something like p +-1.96 sqrt[p(1-p)/n.

Half pint (8oz) milk cartons are filled at a dairy by a filling machine. To provide a check on the machine, a sample of 10 cartons is periodically measured. If the sample mean deviates by more than a certain amount d from the nominal value 8oz, i.e, if [xbar-8]>d, then the machine setting is adjusted. The chance of a false alarm indicating an unnecessary adjustment is to be limited to 1%. Find a formula for d.

I am assuming the Confidence is 99%, is significance level 1%? N=10, so do i do something with a T-test statistic where degrees of freedom is 9?
 
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