Question

A news service conducted a survey of 1004 adults ages 18 years or older in a certain​ country, August 31 - September ​2, 2015. The respondents were​ asked, "Of every tax dollar that goes to the federal​ government, how many cents of each dollar would you say are​ wasted?" Of the 1004 individuals​ surveyed, 34​% indicated that 51 cents or more is wasted. The news service reported that 34​% of all adults in the country 18 years or older believe the federal government wastes at least 51 cents of each dollar​ spent, with a margin of error of 3​% and a 90​% level of confidence. Complete parts ​(a) through​ (e) below:
(a) What is the research objectives?
(b) What is the population?
(c) What is the sample?
(d) List the descriptive statistics

Answer 1

Answer:

a) To assess the perception of adults ages 18 years and older in a certain county on the amount of taxpayer money (cents per dollar) wasted by the government.

b) The population (N) = 1004.

c) The sample size (n) =   1004

d) Descriptive statistics

i. Proportion of respondents (p) who believe 51 cents or more of each dollar is wasted = 0.34.

ii. The proportion of respondents (q) who did not believe that 51 cents or more of each dollar is wasted. This is; q = 1-p. => 1-0.34 => 0.66

Therefore, p = 34% and q = 66%

iii. 34% of 1004 = 341.36 which is rounded down to 341 because we cannot have half human. The measure must be discrete.

iv. 66% of 1006 = 1004 - 341 = 663

This means that;

=> 341 respondents out of 1004 surveyed believe that 51 cents or more of each dollar is wasted

=> 663 respondents out of 1004 surveyed does not believe that 51 cents or more of each dollar is wasted.

NB: The objective of study is only based on those that perceived that government waste taxpayer money. This means that they are the population of interest for this study.

Step-by-step explanation:

a) The research objective is to assess the perception of adults ages 18 years and older in a certain county on the amount of taxpayer money (cent per dollar) wasted by the government.

b) From the question, we are told that the survey covers 1004 adults. This gives us the information of the total number of respondents surveyed for the study. Hence, the population (N) is 1004.

c) The survey was covers 1004 adults age 18 years or older and they all participated in the survey. This implies that the whole population of individuals age 18 or older in the county were surveyed. This is a complete enumeration of the population of interest.

d) We describe the statistics of interest.