Question

1) For a binomial experiment:

Find the sample size required to estimate if you want the estimate to be within 0.01 with 95% confidence.

Round your answer to the next larger integer.

2) For a binomial experiment:

According to a poll, 78% of residents are in favor of a new rec centre. Find the sample size required to estimate the true proportion of residents who are in favor if you want the estimate to be within 0.07 with 95% confidence.

Round your answer up to the next larger integer.

3) For a binomial probability:

A company claims 3% of their switches will be defective. A large contractor wishes to find out if that is true, it was found that 9 of 180 tested were defective.

Determine the test statistic used to perform a hypothesis test regarding this claim with 90% confidence.

Answer to 2 decimal places.

Answer 1

1)

here margin of error E =	0.010
for95% CI crtiical Z          =	1.960	from excel:normsinv((1+0.95)/2)
estimated prop.=p=	0.500
sample size n= p*(1-p)*(z/E)2=	9604	(rounding up)

2)

here margin of error E =	0.070
for95% CI crtiical Z          =	1.960	from excel:normsinv((1+0.95)/2)
estimated prop.=p=	0.780
sample size n= p*(1-p)*(z/E)2=	135	(rounding up)

3)

sample success x   =		9
sample size          n    =		180
std error σp =√(p*(1-p)/n) =		0.0127
sample prop p̂ = x/n=9/180=		0.0500
test statistic z =(p̂-p)/σp=(0.05-0.03)/0.013=		1.57