Question

Calculating Confidence Intervals

1. Suppose that a recent study asked a sample of Kentucky residents

“Do you believe that evolution should be taught in public schools?”

Out of the 100 people surveyed (the survey was given to a random sample) 80 responded yes. Confirm that the sample size is large enough, calculate a 95% confidence interval and interpret the interval. (Round your answer to 4 decimal places)

2. Using the information in question 1 calculate a 90% interval. You do not need to check the sample size or interpret the interval. (Round your answer to 4 decimal places.

3. Using the information in question 1 calculate a 99% interval. You do not need to check the sample size or interpret the interval. (Round your answer to 4 decimal places)

4. Compare your answers from questions 1-3. What happens to a confidence interval when the level of confidence changes but everything else remains the same?

Answer 1

1)

for np=80 and n(1-p)=100-80=20 both are greater than 5 ; hence requirement for normal approximation of binomial distribution are satisfied,.

2)

for 90 % CI value of z=				1.645
margin of error E=z*std error                            =				0.0658
lower confidence bound=sample proportion-margin of error				0.7342
Upper confidence bound=sample proportion+margin of error				0.8658

3)

for 99 % CI value of z=				2.576
margin of error E=z*std error                            =				0.1030
lower confidence bound=sample proportion-margin of error				0.6970
Upper confidence bound=sample proportion+margin of error				0.9030

4)

as we increase/decrease  level of confidence ; width of  confidence interval increases/decreases .