Answer:
a) the sample proportion planning to vote for Candidate Y is
b) the standard error of the sample proportion is ≈ 0.024
c) 95% confidence interval for the proportion of the registered voter population who plan to vote for Candidate Y is (0.353,0.447)
d) 98% confidence interval for the proportion of the registered voter population who plan to vote for Candidate Y is (0.344,0.456)
Step-by-step explanation:
a) The sample proportion planning to vote for Candidate Y is:
b) The standard error of the sample proportion can be found using
SE= where
- p is the sample proportion planning to vote for Candidate Y (0.4)
- N is the sample size (400)
Then SE= ≈ 0.024
c) 95% confidence interval for the proportion of the registered voter population who plan to vote for Candidate Y can be calculated as p±z×SE where
- p is the sample proportion planning to vote for Candidate Y (0.4)
- SE is the standard error (0.024)
- z is the statistic for 95% confidence level (1.96)
Then
0.4±(1.96×0.024)=0.4±0.047 that is (0.353,0.447)
d) 98% confidence interval is similarly
0.4±(2.33×0.024)=0.4±0.056 that is (0.344,0.456) where
2.33 is the statistic for 98% confidence level.