Question

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

In a survey of 1000 large corporations, 240 said that, given a choice between a job candidate who smokes and an equally qualified nonsmoker, the nonsmoker would get the job.

(a) What is the margin of error based on a 95% confidence interval? (Round your answer to three decimal places.)

b)

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

The National Council of Small Businesses is interested in the proportion of small businesses that declared Chapter 11 bankruptcy last year. Since there are so many small businesses, the National Council intends to estimate the proportion from a random sample. Let p be the proportion of small businesses that declared Chapter 11 bankruptcy last year.

In a preliminary random sample of 30 small businesses, it was found that nine had declared Chapter 11 bankruptcy. How many more small businesses should be included in the sample to be 98% sure that a point estimate p̂ will be within a distance of 0.120 from p? (Round your answer up to the nearest whole number.)

b)_______

c)

On the Navajo Reservation, a random sample of 224 permanent dwellings in the Fort Defiance region showed that 70 were traditional Navajo hogans. In the Indian Wells region, a random sample of 139 permanent dwellings showed that 21 were traditional hogans. Let p₁ be the population proportion of all traditional hogans in the Fort Defiance region, and let p₂ be the population proportion of all traditional hogans in the Indian Wells region.

(c) Find a 99% confidence interval for p₁ – p₂. (Use 3 decimal places.)

lower limit
upper limit

d)

"Unknown cultural affiliations and loss of identity at high elevations." These are words used to propose the hypothesis that archaeological sites tend to lose their identity as altitude extremes are reached. This idea is based on the notion that prehistoric people tended not to take trade wares to temporary settings and/or isolated areas. As elevation zones of prehistoric people (in what is now the state of New Mexico) increased, there seemed to be a loss of artifact identification. Consider the following information.

Elevation Zone	Number of Artifacts	Number Unidentified
7000-7500 ft	111	71
5000-5500 ft	141	21

Let p₁ be the population proportion of unidentified archaeological artifacts at the elevation zone 7000-7500 feet in the given archaeological area. Let p₂ be the population proportion of unidentified archaeological artifacts at the elevation zone 5000-5500 feet in the given archaeological area.

(d) Find a 95% confidence interval for p₁ – p₂. (Use 3 decimal places.)

lower limit
upper limit

Answer 1

Solution:-

1)

In a survey of 1000 large corporations, 240 said that, given a choice between a job candidate who smokes and an equally qualified nonsmoker, the nonsmoker would get the job.

(a)The margin of error based on a 95% confidence interval is 0.0265.

$\hat{p}=\frac{x}{n}$

240 p = 1000

0.24

М.Е М.E — гор X /p(1 — р) Ха/2 X п

M.E = 1.96*0.013406

M.E = 0.02647