A poll found that 64% of a random sample of 1076 adults said they believe in gho
ID: 3371156 • Letter: A
Question
A poll found that 64% of a random sample of 1076 adults said they believe in ghosts. Question 1. Find the margin of error z (p) ( 1 P), abbreviated ME, for this poll if we want 90% confidence in our estimate of the proportion of adults who believe in ghosts. ME= (Round to 3 decimal places.) Question 2. Explain what this margin of error means. 2 submissions only The pollsters are 90% confident that the chance a randomly selected adult would believe in ghosts is 0.64 plus or minus ME. 64% plus or minus ME% of adults believe in ghosts 90% of the time. The pollsters are 90% confident that 64% of adults believe in ghosts. The pollsters are 90% confident that the estimate 0.64 plus or minus the margin of error contains the true proportion of adults that believe in ghosts. Question 3. If we want to be 99% confident, will the margin of error be larger or smaller? 1 submission only A 99% confidence interval requires a smaller margin of error. In order to increase confidence, the interval must be narrower. O A 99% confidence interval requires the same margin of error. In order to increase confidence, the interval will stay the same. O A 99% confidence interval requires a larger margin of error. In order to increase confidence, the interval must be wider. Question 4. Find the margin of error needed to be 99% confident. ME= (Round to 3 decimal places.) Question 5. In general, if the sample size and all other aspects remain the same, will smaller margins of error be associated with confidence intervals that have greater levels of confidence or lower levels of confidence? 1 submission only. Smaller margins of error do not affect the confidence level since it is the sample proportion that varies from sample to sample while the true, but unknown, population proportion p is fixed. Smaller margins of error are associated with confidence intervals that have a lower confidence level. Smaller margins of error are associated with confidence intervals that have a greater confidence level.Explanation / Answer
Ans:
1)z for 90% CI is 1.645
Margin of error=1.645*sqrt(0.64*(1-0.64)/1076)=0.024
2)The pollsters are 90% confident that the estimate 0.64+or minus the margin of error contains the true proportion of adults that beleive in ghosts.
(last option is correct)
3)A 99% confidence interval requires a larger margin of error.In order to increase the confidence,the interval must be wider.
4)z value for 99% CI is 2.576
Margin of error=2.576*sqrt(0.64*(1-0.64)/1076)=0.038
5)Smaller the confidence level,smaller the margin of error.
Smaller margins of error are associated with confidence intervals that have a lower confidence level.