A poll showed that 55% 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 500, how many would have said that their country benefits from having a rich class? Assuming the sample size was 500, 275275 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.) A. Yes, the sample size is large enough, since the estimated standard error is nothing, which is greater than or equal to 10. B. No, the sample size is not large enough, since the estimated standard error is nothing, which is less than 10. C. No, the sample size is not large enough, since the expected number of successes is nothing and the expected number of failures is nothing, at least one of which is less than 10. D. Yes, the sample size is large enough, since the expected number of successes is 275275 and the expected number of failures is 225225, 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 %,%. (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 nothing%. (Round to one decimal place as needed.) e. Now assuming the sample size was multiplied by 9 (n=4500) and the percentage was still 55%, how many would have said their country benefits from having a rich class? Assuming the sample size was 4500, nothing 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 %,%. (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 nothing%. (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? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. Yes, when the sample size is multiplied by 9, the width of the interval is divided by 9. B. No, when the sample size is multiplied by 9, the width of the interval is divided by nothing. (Round to the nearest integer as needed.)

A poll showed that 55% 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 500, how many would have said that their country benefits from having a rich class? Assuming the sample size was 500, 275275 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.) A. Yes, the sample size is large enough, since the estimated standard error is nothing, which is greater than or equal to 10. B. No, the sample size is not large enough, since the estimated standard error is nothing, which is less than 10. C. No, the sample size is not large enough, since the expected number of successes is nothing and the expected number of failures is nothing, at least one of which is less than 10. D. Yes, the sample size is large enough, since the expected number of successes is 275275 and the expected number of failures is 225225, 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 %,%. (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 nothing%. (Round to one decimal place as needed.) e. Now assuming the sample size was multiplied by 9 (n=4500) and the percentage was still 55%, how many would have said their country benefits from having a rich class? Assuming the sample size was 4500, nothing 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 %,%. (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 nothing%. (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? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. Yes, when the sample size is multiplied by 9, the width of the interval is divided by 9. B. No, when the sample size is multiplied by 9, the width of the interval is divided by nothing. (Round to the nearest integer as needed.)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.2: Arithmetic Sequences

Problem 67E

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Related questions

Question

A poll showed that

55%

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

500,

how many would have said that their country benefits from having a rich class?

Assuming the sample size was

500,

275275

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.)

Yes, the sample size is large enough, since the estimated standard error is

nothing,

which is greater than or equal to 10.

No, the sample size is not large enough, since the estimated standard error is

nothing,

which is less than 10.

No, the sample size is not large enough, since the expected number of successes is

nothing

and the expected number of failures is

nothing,

at least one of which is less than 10.

Yes, the sample size is large enough, since the expected number of successes is

275275

and the expected number of failures is

225225,

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

%,%.

(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

nothing%.

(Round to one decimal place as needed.)

e. Now assuming the sample size was multiplied by

(n=4500)

and the percentage was still

55%,

how many would have said their country benefits from having a rich class?

Assuming the sample size was

4500,

nothing

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

%,%.

(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

nothing%.

(Round to one decimal place as needed.)

h. When the sample size is multiplied by

is the width of the interval divided by

If not, what is it divided by? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

Yes, when the sample size is multiplied by

the width of the interval is divided by

No, when the sample size is multiplied by

the width of the interval is divided by

nothing.

(Round to the nearest integer as needed.)

Expert Solution

Step 1

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Step 2

If x denotes the number of cases favourable to an event in a sample of size n, then the sample proportion is, p̂ = x/n.

It is given that, the sample size is n = 500 and the poll showed that 55% of randomly surveyed adults in a certain country said their country benefits from having a rich class. Thus, p̂ = 0.55.

Thus, 275 (= np̂ = (500)(0.55)) would have said that their country benefits from having a rich class.

Step 3

The assumptions and conditions under which a claim about a population proportion can be tested, are as follows:

The sample must be collected using simple random sampling, to ensure that the observations are all independent of one another and there is no unnecessary bias.

Here, it is assumed that the adults are selected randomly.

There must be at least 10 sample units recording success, and 10 sample units recording failure, in the study.

Thus, np̂ = 500 ∙ (0.55) = 275 > 10, and n(1 – p̂) = 500 ∙ (1 – 0.55) = 225 > 10.

Hence, Yes, the sample size is large enough, to apply the CLT since the expected number of successes is 275 and the expected number of failures is 225, both of which are greater than or equal to 10.

The correct option is D.

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