Suppose you had been in charge of designing the study. what sample size would be needed to construct a margin of error of 2% with 95% confidence? use the prior point estimate of p* = 0.15 for this calculation. round up to the nearest whole number. (for example, 144.1 would round to 145)

1225

Step-by-step explanation:

hihi. So the equation for MoE is (z*) * SE. The z* for a 95% Confidence is one you should have memorized but for repeatability sake you can always just do an inverse Norm to find the z* for these types of applications. To do so, you can always type this command into your calculator: invNorm(conf + (1-conf)/2, 0, 1).

(When I say conf here I am referring to the confidence level as a decimal).

All that's left is the Standard Error or SE to be short. Since you gave a p* estimate then we can use the equation for SE when dealing with proportions/percents which is sqrt(p(1-p) / n) where p is the proportion and n is the sample size, which we are solving for. Once you have this established it's a basic multi-step solve for n which comes out to be 1225 after rounding.

A side note, the included picture is a bit messy due to my refusal to round when doing these kinds of problems. Rounding errors are more common than you think

distance covered by pamela in 9 l of fuel = 99km

let us apply unitary method here.

distance covered by pamela in 1 l of fuel =99/9 =11 km

now let us find distance covered by pamela if she has 12 l of fuel.

distance covered in 12 l = distance covered in 1 l of fuel * 12

we know that distance covered by here in 1 l is 11 km.

so distance covered in 12 l of fuel = 11*12 = 132 km.