A random sample of 1022 adults in a certain large country was asked \"Do you pre

Question

A random sample of 1022 adults in a certain large country was asked "Do you pretty much think televisions are a necessity or a luxury you could do without? Of the 1022 adults surveyed, 533 indicated that televisions are a luxury they could do without. Complete parts (a) through (e) below. andard normal distrib Click here to view the standard normal distribution table ipage 2) (a) Obtain a point estimate for the population proportion of adults in the country who believe that televisions are a luxury they could do without. (Round to three decimal places as needed.) (b) Verity that the requirements for constructing a confidence interval about p are satisfied The sample L-disDwhich is a simple random sample, the value of | is | |, which is | 10, and the | less than or equal to 5% of the Round to three decimal places as needed.) c Construct and interpret a 95% confidence inter a for the population proportion o adults in the country who believe a televisions are a luuy ey ou within your choice (Type integers or decimals rounded to three decimal places as needed. Use ascending order.) OA. We are % confident proportion of adults in the country who believe that televisions are a luxury they could do without is between and do e out elect co rec ace w an nan answer s O B. There is a % chance the proportion of adults in the country who believe that televisions are a luxury the could do without is between Idi Is it noss ihla that a sunarmaioritv mnra than 60%) of adults in the ciintrv haliAV llnirv the cnuld do without? Is it likale? Click to select your answers). and a that telavisinn is a

Explanation / Answer

a. The point estimate of population proportion, p of the adults in the country whp believe that television is a luxuary theu could do without is sample proportion phat.

phat=#of events/# of trials=533/1022=0.522

b. Since, a random sample of 1022 adults have been selected, therefore, the sample is a simple random sample, the value of np(1-p)=1022(0.522)(1-0.522)=255 which is greater than 10 and the sample is less than or equal to 5% of the population.

c. The 95% c.i for the population proportion, p of adults in the country who beleive that television is a luxuray they could do without is as follows: phat+-zalpha/2 sqrt[phat(1-phat)/n], where, phat is sample proportion, zalpha/2 is z critical at alpha/2 and n is sample size.

0.522+-1.96sqrt[0.522(1-0.522)/1022]

=(0.492, 0.553)

Thus, one can be 95% confident that the tru epopulation proportion of adults who believ ethat television is a luxuray they could live without is between (0.492,0.553). Option A is correct answer, while B is wrong in sense, that according to 95% confidence interval definition, the true population parameter will fall within the interval estimates 95% of time.

d. The 95% confidence interval does not contain p=0.60, therefore, conclude that it is likely that a supermajority of adults in the country believe that television is a luxury they could do without.

Answer> likely, donot contain 0.60.

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