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Chapter 10: Q. AP3.22 (page 704)

A random sample of size n will be selected from a population, and the proportion p^3051526=0.200=20.0%p^ of those in the sample who have a Facebook page will be calculated. How would the margin of error for a 95% confidence interval be affected if the sample size were increased from 50to200 and the sample proportion of people who have a Facebook page is unchanged?

a. It remains the same.

b. It is multiplied by 2.

c. It is multiplied by 4.

d. It is divided by 2.

e. It is divided by 4.

Short Answer

Expert verified

The correct answer is:

d. It is divided by2

Step by step solution

01

 Step 1: Given information 

We have to tell about confidence interval would be affected if the sample size were increased.

02

Explanation 

  • The term that comes to me while thinking about this issue is proportion. What should be considered is the proportional margin of error.
  • It's critical to comprehend the link between 'n' and the margin of error. When 'n' is in the denominator, the margin of error reduces at a square root rate as n rises.
  • The number four can be found in the square root of four, which is two. The new margin of error is half that of the previous one.

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Most popular questions from this chapter

A 96% confidence interval for the proportion of the labor force that is unemployed in a certain city is (0.07,0.10). Which of the following statements is true?

a. The probability is 0.96 that between 7%and10% of the labor force is unemployed.

b. About 96% of the intervals constructed by this method will contain the true proportion of the labor force that is unemployed in the city.

c. In repeated samples of the same size, there is a 96% chance that the sample proportion will fall between 0.07and0.10.

d. The true rate of unemployment in the labor force lies within this interval 96% of the time.

e. Between 7%and10%of the labor force is unemployed 96% of the time.

Drive-thru or go inside? Many people think it’s faster to order at the drive-thru than to order inside at fast-food restaurants. To find out, Patrick and William used a random number generator to select10times over a 2‐week period to visit a local Dunkin’ Donuts restaurant. At each of these times, one boy ordered an iced coffee at the drive-thru and the other ordered an iced coffee at the counter inside. A coin flip determined who went inside and who went to the drive-thru. The table shows the times, in seconds, that it took for each boy to receive his iced coffee after he placed the order.

Do these data provide convincing evidence at the α=0.05level of a difference in the true mean service time inside and at the drive-thru for this Dunkin’ Donuts restaurant?

Treating AIDS The drug AZT was the first drug that seemed effective in delaying

the onset of AIDS. Evidence for AZT’s effectiveness came from a large randomized

comparative experiment. The subjects were 870volunteers who were infected with HIV,

the virus that causes AIDS, but did not yet have AIDS. The study assigned 435of the

subjects at random to take 500milligrams of AZT each day and another 435to take a

placebo. At the end of the study, 38of the placebo subjects and 17of the AZT subjects

had developed AIDS.

a. Do the data provide convincing evidence at the α=0.05level that taking AZT lowers the proportion of infected people like the ones in this study

who will develop AIDS in a given period of time?

b. Describe a Type I error and a Type II error in this setting and give a consequence of

each error.

A random sample of size nwill be selected from a population, and the proportion of those in the sample who have a Facebook page will be calculated. How would the margin of error for a 95%confidence interval be affected if the sample size were increased from 50to 200?

(a) It remains the same.

(b) It is multiplied by 2.

(c) It is multiplied by 4.

(d) It is divided by 2.

(e) It is divided by 4.

In an experiment to learn whether substance M can help restore memory, the brains of 20rats were treated to damage their memories. First, the rats were trained to run a maze. After a day, 10rats (determined at random) were given substance M and 7of them succeeded in the maze. Only 2of the 10control rats were successful. The two-sample z test for the difference in the true proportions

a. gives z=2.25,P<0.02 .

b. gives z=2.60,P<0.005 .

c. gives z=2.25,P<0.04 but not<0.02

d. should not be used because the Random condition is violated.

e. should not be used because the Large Counts condition is violated.
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