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An Internet article reports on results of a study completed in 2004 by psychologists at universities in Washington and Oregon: 65 Percent of Children Have Had an Imaginary Companion. The researchers originally recruited 152 preschoolers, ages5 and 4, and their parents several years ago. Each child and parents were interviewed separately about imaginary companions. . 9.24
years later, 100 of those children Threes and 50 boys) and their parents unteered for the newly published study. hildren and their parents again were The children and their pa rviewed separately about imaginary rompanions. . I Children were considered to have imaginary companions if they said hey had one and provided a description of 19 Some examples cited in a newspaper report of the study included Rose (an invisible 9-year-old squirrel), Skateboard Guy (an invisible 11-year-old who lived in a boys pocket and popped up at boring moments to do tricks on his skateboard) and Elephant (a 7-inch-tall pachyderm that wore a tank top and shorts and sometimes was mean). a. Is there reason to believe that the 100 it. children (with parents) who volunteered to continue in the study 3 years after the initial interview were no different from the 52 children who abstained? If not, would you expect those 100 children to be more likely or less likely to have imaginary companions? b. The researchers focused on children up to the age of 7. Use the reported proportion (0.65) and the sample size (100) to construct a 95% confidence interval for the proportion of all such children who have an imaginary companion, rounding your margin of error to the nearest hundredth. c. There are roughly 20,000,000 children aged three to seven in the United States. Use your confidence interval in part (b) to give a range for the umber of imaginary friends they have altogether Note that some children may have more an one imaginary friend, and others may share the same imaginary friend, but we will disregard those here.)
math   Statistics-And-Probability   
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An Swc Grtven -ttat, rリyes, we have no reason to believe that those 52. people who absteined baom port io patig alrd 90-km seasons that would ebtecta 8) we wont to use the tanmela 术 uhere n is he saumple stze, P is Ho Saple propotion ardzs the oppor萍ate valoe -enthe desto ed Confidence. s n this case P=B50, 65) n=loo, and -960 0cenlidnte ideval to 0.65 + 1.96oes(1-04s) 1o0 0.65 + 1.96 ) l0o65+0-0935 7435 0.65- 935 o. 556S- 0.56 So boo this anstoen we want tolonge uo fntonvel land in answen B to one on the nnben o pyoption inoy erienols. vo do thie we snold imply molpl States,in thrs case 90,000,000s twould be o.56 2X1 11,oo,ooo 4,800,000 bound wovld be 1s miltion im ogivo Paenls and thelouwt boond uwod be l illdon

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