Question

1.) A back-of-the-envelope calculation for a 95% CI for the

population mean mu is

[xbar - 2*SE , xbar + 2*SE]

where xbar is the sample mean and SE is the standard error

of the sample mean. When xbar = 3.1 and SE 1.5,

what is the left end point of a back-of-the-envelope 95%

confidence interval for the population mean?

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2.) Suppose that 32 of the 1500 people that received an email we sent, clicked on the offer image. What is the estimate for the left end point of a 95% confidence interval for the proportion of people in the population that will click on an offer that we send them? (Round to 3 digits after the decimal point)

Answer 1

1)left end point of a back-of-the-envelope 95% confidence interval for the population mean =3.1-2*1.5 =0.1

2)

sample success x =		32
sample size          n=		1500
sample proportion p̂ =x/n=		0.0213
std error se= √(p*(1-p)/n) =		0.0037

estimate for the left end point of a 95% confidence interval for the proportion of people in the population that will click on an offer that we send them =0.0213-2*0.0037 =0.014