Question

In a random sample of 251 Ewoks, it was found that 103 were superstitious.

1. What percentage of Ewoks polled are superstitious?

2. What is the standard error for the estimate of the proportion of all Ewoks that are superstitious?

3. Report the 99% confidence interval for the proportion of all superstitious Ewoks?

4. According to Princess Leia, the majority of Ewoks are superstitious. Is she correct explain?

Answer 1

given that

sample size =n=251 x=103

1.

proportion is given by

so required % is 0.4104*100 =41.04%

2)

the standard error is given by

3)

now 99% confidence interval is given by

so interval is (0.3304,0.4904)

4)

if we look at the confidence interval in part (3) the upper bound is 0.49 and that means 99% of times proportion will be less than 0.5 hence she is incorrect