Hypotheses Testing

Question

A recent poll stated that out of the 40 people interviewed, 22 of them drove to work. Create a 95% confidence interval for the true percentage of people who drive to work.

Pick the correct distribution (tcv or zcv) and calculate E and CI

Answer 1

You could also purchase MegaStat for about 20.00 and use Confidence Interval - proportion and enter

.55 for p

40 for n

set at confidence level at 95%

The output would be:

.396 or 39.6 lower confidence limit

.704 or 70.4 upper confidence limit

.154 or 15.4 is the margin of error

Depends on what your instructor wants. Use a T1-84 calculator or a statistical software program.

Answer 2

Use the Z-distribution since the sample size is large enough for a Normal approximation.

p-hat, the sample proportion, is 0.55 (22/40)

n is 40

Using 1-PropZInt on a TI-84 calculator, where x is 22, n is 40, and the C-Level is 0.95, the calculated confidence interval is (39.6%, 70.4%)

E (margin of error) is calculated by taking the upper bound and subtracting p-hat from it (or by taking p-hat and subtracting out the lower bound). The margin of error is 15.4%.

Hope this was helpful.