Question

A poll showed that 37% of randomly surveyed adults in a certain country said their country benefits from having a rich class. Complete parts​ (a) through​ (h) below.

a. Assuming the sample size was 300, Answer_____ people in the sample would have said that their country benefits from having a rich class.Round to the nearest integer as​ needed.)

b. Is the sample size large enough to apply the Central Limit​ Theorem? Explain. Assume the other conditions for using the CLT are met. Select the correct choice below and fill in the answer​ box(es) to complete your choice(Round to the nearest integer as​ needed.)

B.​Yes, the sample size is large​ enough, since the expected number of successes is Answer ____ and the expected number of failures is Answer ____, both of which are greater than or equal to 10.

c. Find a​ 95% confidence interval for the percent that believe that their country benefits from having a rich​ class, using the numbers from part​ (a).

The​ 95% confidence interval is Answer______%​(Round to one decimal place as​ needed.)

d. Find the width of the interval you found in part​ (c) by subtracting the lower boundary from the upper boundary.

The width of the interval is Answer _____.​(Round to one decimal place as​ needed.)

e. Now assuming the sample size was multiplied by 99 ​(n=2700​) and the percentage was still 37​%,how many would have said their country benefits from having a rich​ class?

Assuming the sample size was Answer ____, ___ would have said they were thriving. ​(Round to the nearest integer as​ needed.)

f. Find a​ 95% confidence​ interval, using the numbers from part​ (e).The​ 95% confidence interval is Answer (___, ____).. ​(Round to one decimal place as​ needed.)

g. What is the width of the interval you found in part​ (f) The width of the interval is Answer ____%.​(Round to one decimal place as​ needed.)

h. When the sample size is multiplied by 9 is the width of the interval divided by 9​? If​ not, what is it divided​ by? .

No, when the sample size is multiplied by 9, the width of the interval is divided b Answer ___ the nearest integer as​ needed.)

Answer 1

Given, - n = 300 P = 0.37 aj xsmp : 300 x 0.37 People in the sample would have said that that contry benefits from having a rich clay. bo Yes, the sample size is large enough, since the estimate no of succes is np: 111 Ę Expected no. of failures =n(1-P) = 889 both of which are greater than 10. 1. c) 95% confidence internal Côt z dy J PCI-P) from 2-table 7 = 1.96 (0.37 + 1.96 5 0.37x0.63 ) 300 3 (0.37 ¢ 0.05463 ) - (0.4246 , 0.3153)

Co do width d) width = Upper boundary - lower boundary = 0.4246 - 0.3153 = 0.1093 e) . if no 2700 P: 0:37 x : np: 2700 * 0.37 [999] would have said they were thrining f, 95% confidence interval is _AGAZMOD (P+ 2 SP CIP A L 5 (0.34 + 1.96 0.37 0.63 2700 -) (0.37 + 0.01821) CALE ) (0.3882 , 0.3518 )

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