The 2017 Chapman University Survey of American Fears asked a random sample of 1207 adult Americans if they believe that aliens have come to earth in modern times and 26% replied "yes". (assume independence)
For each part, show the work by hand OR include what you plugged into the technology and a picture of the technology output.
Part 1: List the conditions for the Central Limit Theorem and check that they have been met.
Part 2: Tell the equation for finding Standard Error in symbolic format.
Part 3: Calculate the standard error. Give your answer as a decimal rounded to 4 decimal places and as a percentage rounded to two decimal places.
Part 4: What is the equation in symbolic format for finding the margin of error for the 95% confidence interval?
Part 5: Calculate the margin of error for this 95% confidence interval? Give your answer as a decimal rounded to 4 decimal places and as a percentage rounded to two decimal places.
Part 6: What is the equation in symbolic format for finding the confidence interval?
Part 7: Calculate the 95% confidence interval for the proportion of all Americans who believe that aliens have come to Earth in modern times. Give your final answer first as an interval with the answer represented as a decimal rounded to four decimal places. Then interpret the Confidence interval.
Part 8: A similar poll was conducted in 2016 which found that 24.7% of Americans believed that aliens have come to earth in modern times. Based on your confidence interval, can you conclude that the proportion of Americans who "believe" has increased since 2016?