A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 2 percentage points with 99% confidence if (a) he uses a previous estimate of 25%? (b) he does not use any prior estimates?

a) We need a sample size of at least 3109.

b) We need a sample size of at least 4145.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

In which

z is the zscore that has a pvalue of .

The margin of error is:

99% confidence level

So , z is the value of Z that has a pvalue of , so .

(a) he uses a previous estimate of 25%?

we need a sample of size at least n.

n is found when . So

We need a sample size of at least 3109.

(b) he does not use any prior estimates?

When we do not use any prior estimate, we use

So

Rounding up

We need a sample size of at least 4145.

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.