Question

A Gallup poll found that 493 of 1050 adult Americans believe it is the responsibility of the federal government to make sure all Americans have healthcare coverage.

• What is the sample in this study? What is the population of interest?

• What is the variable of interest in this study? Is it qualitative or quantitative?

• Based on the results of this study, obtain a point estimate for the proportion of adult Americans who believe it is the responsibility of the federal government to make sure all Americans have healthcare coverage.

• Explain why the point estimate in #3 is a statistic? Why is it a random variable?

• Construct and interpret a 90% confidence interval for the proportion of adult Americans who believe it is the responsibility of the federal government to make sure all Americans have healthcare coverage.

• Name two things that might be done to increase the precision of the confidence interval?

Answer 1

A Gallup poll found that 493 of 1050 Adult Americans believes that it is Susponsibility of federal Govt. to make el sure that all Americans have heathcare coverage Here in this question sample is those 1050 adult Americans who are surveyed by the poll. Owe population of interest is All adult Americans AMMYYYYYYYYYYYYTY , Here in this study the variable is the peloportion of adult American, who believes that it is duesponsibility of Federal Glost to make sure that all Americans have healthcare coverage. As preoportion is a ratio of two number hence the variable is quantitative. Now, the point estimate from Astapo populatón priobortion of adulla American, is, Ñ . Sample Proportion e No. of respondent Total number of people observed

493 1050 . 2 = 0 +67. D A Statistic is a clareceruistic of a sample Feue Hally is used to estimată the Value of a population parameters Here, 2 is a sample proportion, which is a charesteristic of a sample. and also, we want to estimate population Proportion ww with this proportion So, Ê is a statistic. I NOW, a landom variable is a variable that does not have any value unhl some experiment 's performed. defined in advance That is, it is not liere, Gallup poll sevireyed 1050 adult American and found 493 people believe the fact Hence il- is a Handom variable. Now, we have to construela 90% for population confidence integal feroportion. Here we use ztest as sample "The formula is given by, ? I Z* JACKP)

The value of z* at90% confidence levelis -. 7* 2.1645 I. Cha 0:469 1 44645 v 1050 06:469-0°025 ; 00469+0025) (0:444,0-494) CI= 0'469 + 1645 10:469 (1.0469)