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.

(a) If no preliminary sample is taken to estimate *p*, how large a sample is necessary to be 99% sure that a point estimate p̂ will be within a distance of 0.08 from *p*? (Round your answer up to the nearest whole number.)

?? small businesses

?? small businesses

(b) In a preliminary random sample of 30 small businesses, it was found that eleven had declared Chapter 11 bankruptcy. How many *more* small businesses should be included in the sample to be 99% sure that a point estimate p̂ will be within a distance of 0.080 from *p*? (Round your answer up to the nearest whole number.)

?? more small businesses

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

A random sample of 5240 permanent dwellings on an entire reservation showed that 1690 were traditional hogans.

(a) Let *p* be the proportion of all permanent dwellings on the entire reservation that are traditional hogans. Find a point estimate for *p*. (Round your answer to four decimal places.)

(b) Find a 99% confidence interval for *p*. (Round your answers to three decimal places.)

lower limit | |

upper limit |

Give a brief interpretation of the confidence interval.

1% of all confidence intervals would include the true proportion of traditional hogans.99% of all confidence intervals would include the true proportion of traditional hogans. 99% of the confidence intervals created using this method would include the true proportion of traditional hogans.1% of the confidence intervals created using this method would include the true proportion of traditional hogans.

(c) Do you think that *np* > 5 and *nq* > 5 are satisfied for this problem? Explain why this would be an important consideration.

Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial.No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial. Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal.No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal.

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

Case studies showed that out of 10,732 convicts who escaped from certain prisons, only 7864 were recaptured.

(a) Let *p* represent the proportion of all escaped convicts who will eventually be recaptured. Find a point estimate for *p*. (Round your answer to four decimal places.)

(b) Find a 99% confidence interval for *p*. (Round your answers to three decimal places.)

lower limit | |

upper limit |

A random sample of 5060 permanent dwellings on an entire reservation showed that 1697 were traditional hogans.

(a) Let *p* be the proportion of all permanent dwellings on the entire reservation that are traditional hogans. Find a point estimate for *p*. (Round your answer to four decimal places.)

(b) Find a 99% confidence interval for *p*. (Round your answer to three decimal places.)

lower limit | ? |

upper limit | ? |

A random sample of medical files is used to estimate the proportion *p* of all people who have blood type B.

(a) If you have no preliminary estimate for *p*, how many medical files should you include in a random sample in order to be 85% sure that the point estimate p̂ will be within a distance of 0.04 from *p*? (Round your answer up to the nearest whole number.)

medical files

medical files

(b) Answer part (a) if you use the preliminary estimate that about 7 out of 90 people have blood type B.

medical files

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

In a random sample of 68 professional actors, it was found that 36 were extroverts.

(a) Let p represent the proportion of all actors who are extroverts. Find a point estimate for p. (Round your answer to four decimal places.)

(b) Find a 95% confidence interval for p. (Round your answers to two decimal places.)

lower limit

upper limit

Give a brief interpretation of the meaning of the confidence interval you have found.

We are 5% confident that the true proportion of actors who are extroverts falls within this interval.

We are 95% confident that the true proportion of actors who are extroverts falls outside this interval.

We are 5% confident that the true proportion of actors who are extroverts falls above this interval.

We are 95% confident that the true proportion of actors who are extroverts falls within this interval.

(c) Do you think the conditions n·p > 5 and n·q > 5 are satisfied in this problem? Explain why this would be an important consideration.

No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal.

Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal.

Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial.

No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial.

In a marketing survey, a random sample of 984 supermarket shoppers revealed that 274 always stock up on an item when they find that item at a real bargain price.

lower limit =

upper limit =

**Give a brief explanation of the meaning of the interval.**

a.) We are 95% confident that the true proportion of shoppers who stock up on bargains falls within this interval.

b.) We are 5% confident that the true proportion of shoppers who stock up on bargains falls above this interval.

c.) We are 95% confident that the true proportion of shoppers who stock up on bargains falls outside this interval.

d.) We are 5% confident that the true proportion of shoppers who stock up on bargains falls within this interval.

a.) Report the margin of error.

b.) Report p̂ along with the margin of error.

c.) Report the confidence interval.Report p̂.

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

______(blank).

In a random sample of 69 professional actors, it was found that 39 were extroverts.

Let *p* represent the proportion of all actors who are extroverts. Find a point estimate for *p*. (Round your answer to four decimal places.)

Find a 95% confidence interval for *p*. (Round your answers to two decimal places.)

lower limit

upper limit

Give a brief interpretation of the meaning of the confidence interval you have found.

We are 95% confident that the true proportion of actors who are extroverts falls within this interval.We are 95% confident that the true proportion of actors who are extroverts falls outside this interval. We are 5% confident that the true proportion of actors who are extroverts falls within this interval.We are 5% confident that the true proportion of actors who are extroverts falls above this interval.

Do you think the conditions *n*·*p* > 5 and *n*·*q* > 5 are satisfied in this problem? Explain why this would be an important consideration.

No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal.Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal. Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial.No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial.

A random sample of 5967 physicians in Colorado showed that 3116 provided at least some charity care (i.e., treated poor people at no cost).

(a) Let *p* represent the proportion of all Colorado physicians who provide some charity care. Find a point estimate for *p*. (Round your answer to four decimal places.)

(b) Find a 99% confidence interval for *p*. (Round your answers to three decimal places.)

lower limit:

upper limit:

Give a brief explanation of the meaning of your answer in the context of this problem.

We are 99% confident that the true proportion of Colorado physicians providing at least some charity care falls outside this interval.

We are 99% confident that the true proportion of Colorado physicians providing at least some charity care falls within this interval.

We are 1% confident that the true proportion of Colorado physicians providing at least some charity care falls above this interval.

We are 1% confident that the true proportion of Colorado physicians providing at least some charity care falls within this interval.

(c) Is the normal approximation to the binomial justified in this problem? Explain.

No; *np* < 5 and *nq* > 5.

No; *np* > 5 and *nq* < 5.

Yes; *np* < 5 and *nq* < 5.

Yes; *np* > 5 and *nq* > 5.

How hard is it to reach a businessperson by phone? Let *p* be the proportion of calls to businesspeople for which the caller reaches the person being called on the *first* try.

(a) If you have no preliminary estimate for *p*, how many business phone calls should you include in a random sample to be 80% sure that the point estimate p̂ will be within a distance of 0.03from *p*? (Round your answer up to the nearest whole number.)

________phone calls

________phone calls

(b) A report states that businesspeople can be reached by a single phone call approximately 14% of the time. Using this (national) estimate for *p*, answer part (a). (Round your answer up to the nearest whole number.)

________phone calls

Case studies showed that out of 10,749 convicts who escaped from certain prisons, only 7347 were recaptured.

(a) Let *p* represent the proportion of all escaped convicts who will eventually be recaptured. Find a point estimate for *p*. (Round your answer to four decimal places.)

(b) Find a 99% confidence interval for *p*. (Round your answers to three decimal places.)

lower limit | |

upper limit |

Give a brief statement of the meaning of the confidence interval.

We are 1% confident that the true proportion of recaptured escaped convicts falls within this interval.We are 1% confident that the true proportion of recaptured escaped convicts falls above this interval. We are 99% confident that the true proportion of recaptured escaped convicts falls outside this interval.We are 99% confident that the true proportion of recaptured escaped convicts falls within this interval.

(c) Is use of the normal approximation to the binomial justified in this problem? Explain.

Yes; *np* > 5 and *nq* > 5.No; *np* > 5 and *nq* < 5. Yes; *np* < 5 and *nq* < 5.No; *np* < 5 and *nq* > 5.

A random sample of 5240 permanent dwellings on an entire reservation showed that 1585 were traditional hogans.

(a) Let *p* be the proportion of all permanent dwellings on the entire reservation that are traditional hogans. Find a point estimate for *p*. (Round your answer to four decimal places.)

(b) Find a 99% confidence interval for *p*. (Round your answer to three decimal places.)

lower limit | |

upper limit |

Give a brief interpretation of the confidence interval.

99% of the confidence intervals created using this method would include the true proportion of traditional hogans.1% of the confidence intervals created using this method would include the true proportion of traditional hogans. 99% of all confidence intervals would include the true proportion of traditional hogans.1% of all confidence intervals would include the true proportion of traditional hogans.

(c) Do you think that *np* > 5 and *nq* > 5 are satisfied for this problem? Explain why this would be an important consideration.

Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial.No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal. No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial.Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal.

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.

(a) If no preliminary sample is taken to estimate *p*, how large a sample is necessary to be 98% sure that a point estimate p̂ will be within a distance of 0.10 from *p*? (Round your answer up to the nearest whole number.)

__________small businesses

__________small businesses

(b) In a preliminary random sample of 30 small businesses, it was found that twelve 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 0.100 from *p*? (Round your answer up to the nearest whole number.)

____________more small businesses

In a random sample of 60 professional actors, it was found that 45 were extroverts.

Let *p* represent the proportion of all actors who are extroverts. Find a point estimate for *p*. (Round your answer to four decimal places.)

Find a 95% confidence interval for *p*. (Round your answers to two decimal places.)

lower limit _________

upper limit _________

Give a brief interpretation of the meaning of the confidence interval you have found.

We are 5% confident that the true proportion of actors who are extroverts falls above this interval.

We are 95% confident that the true proportion of actors who are extroverts falls within this interval.

We are 95% confident that the true proportion of actors who are extroverts falls outside this interval.

We are 5% confident that the true proportion of actors who are extroverts falls within this interval.

Do you think the conditions *n*·*p* > 5 and *n*·*q* > 5 are satisfied in this problem? Explain why this would be an important consideration.

Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial.

Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal.

No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal.

No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial.

In a random sample of 62 professional actors, it was found that 36 were extroverts.

Let *p* represent the proportion of all actors who are extroverts. Find a point estimate for *p*. (Round your answer to four decimal places.)

Find a 95% confidence interval for *p*. (Round your answers to two decimal places.)

lower limit:

upper limit:

Give a brief interpretation of the meaning of the confidence interval you have found.

a. We are 5% confident that the true proportion of actors who are extroverts falls within this interval.

b. We are 95% confident that the true proportion of actors who are extroverts falls within this interval.

c. We are 5% confident that the true proportion of actors who are extroverts falls above this interval.

d. We are 95% confident that the true proportion of actors who are extroverts falls outside this interval.

Do you think the conditions *n*·*p* > 5 and *n*·*q* > 5 are satisfied in this problem? Explain why this would be an important consideration.

a. Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial.

b. Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal.

c. No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal.

d.No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial.

In a random sample of 64 professional actors, it was found that 44 were extroverts.

(a)

Let *p* represent the proportion of all actors who are extroverts. Find point estimates for *p* and *q*. (Round your answer to four decimal places.)

p̂=q̂=

(b)

Find a 95% confidence interval for *p*.

Find the maximal margin of error. (Round your answer to two decimal places.)

Report the bounds from the 95% confidence interval for *p*. (Round your answers to two decimal places.)

lower limitupper limit

In a survey of 1000 large corporations, 242 said that, given a choice between a job candidate who smokes and an equally qualified nonsmoker, the nonsmoker would get the job.

(a) Let *p* represent the proportion of all corporations preferring a nonsmoking candidate. Find a point estimate for *p*. (Round your answer to four decimal places.)

(b) Find a 0.95 confidence interval for *p*. (Round your answers to three decimal places.)

lower limit | |

upper limit |

(c) As a news writer, how would you report the survey results regarding the proportion of corporations that would hire the equally qualified nonsmoker?

Report p̂.Report the margin of error. Report p̂ along with the margin of error.

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

A random sample of 5832 physicians in Colorado showed that 3143 provided at least some charity care (i.e., treated poor people at no cost).

(a) Let *p* represent the proportion of all Colorado physicians who provide some charity care. Find a point estimate for *p*. (Round your answer to four decimal places.)

(b) Find a 99% confidence interval for *p*. (Round your answers to three decimal places.)

lower limit | |

upper limit |

For this problem, carry at least four digits after the decimal in your calculations.

In a random sample of 70 professional actors, it was found that 36 were extroverts.

(a)

Let *p* represent the proportion of all actors who are extroverts. Find point estimates for *p* and *q*. (Round your answer to four decimal places.)

p̂=q̂=

(b)

Find a 94% confidence interval for *p*.

Find the maximal margin of error. (Round your answer to two decimal places.)

Report the bounds from the 94% confidence interval for *p*. (Round your answers to two decimal places.)

lower limitupper limit

Give a brief interpretation of the meaning of the confidence interval you have found.

We are 6% confident that the true proportion of actors who are extroverts falls above this interval.We are 6% confident that the true proportion of actors who are extroverts falls within this interval. We are 94% confident that the true proportion of actors who are extroverts falls within this interval.We are 94% confident that the true proportion of actors who are extroverts falls outside this interval.

(c)

Do you think the conditions *np* > 5 and *nq* > 5 are satisfied in this problem? Explain why this would be an important consideration.

No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal.No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial. Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal.Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial.

For this problem, carry at least four digits after the decimal in your calculations.

A random sample of medical files is used to estimate the proportion *p* of all people who have blood type B.

(a)

If you have no preliminary estimate for *p*, how many medical files should you include in a random sample in order to be 82% sure that the point estimate p̂ will be within a distance of 0.06 from *p*?

Find the critical value for 82% confidence level,

z_{0.82},

and find the specified maximal error of estimate, *E*. (Round your answers to two decimal places.)

z_{0.82}

=*E*=

Compute the minimal sample size *n* for estimating the proportion *p* of all people who have blood type B under these restrictions. (Round your answer to a whole number.)

(b)

Answer part (a) only this time use the preliminary estimate that about 15 out of 87 people have blood type B. (Round your proportions to three decimal places and your minimum sample size to a whole number.)

In a random sample of 66 professional actors, it was found that 36 were extroverts.

(a)Let *p* represent the proportion of all actors who are extroverts. Find point estimates for *p* and *q*. (Round your answer to four decimal places.)

p̂=

q̂=

(b)Find a 95% confidence interval for *p*.

Find the maximal margin of error. (Round your answer to two decimal places.)

Report the bounds from the 95% confidence interval for *p*. (Round your answers to two decimal places.)

lower limit

upper limit

In a random sample of 61 professional actors, it was found that 36 were extroverts.

lower limit

upper limit

Give a brief interpretation of the meaning of the confidence interval you have found:

We are 95% confident that the true proportion of actors who are extroverts falls within this interval.

We are 5% confident that the true proportion of actors who are extroverts falls above this interval.

We are 5% confident that the true proportion of actors who are extroverts falls within this interval.

We are 95% confident that the true proportion of actors who are extroverts falls outside this interval.

Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal.

No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial.

No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal.

Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial.

In a marketing survey, a random sample of 992 supermarket shoppers revealed that 274 always stock up on an item when they find that item at a real bargain price.

Let *p* represent the proportion of all supermarket shoppers who always stock up on an item when they find a real bargain. Find a point estimate for *p*. (Enter a number. Round your answer to four decimal places.)

Find a 95% confidence interval for *p*. (For each answer, enter a number. Round your answers to three decimal places.)

lower limit

upper limit

Give a brief explanation of the meaning of the interval.

We are 95% confident that the true proportion of shoppers who stock up on bargains falls within this interval.We are 5% confident that the true proportion of shoppers who stock up on bargains falls above this interval. We are 5% confident that the true proportion of shoppers who stock up on bargains falls within this interval.We are 95% confident that the true proportion of shoppers who stock up on bargains falls outside this interval.

As a news writer, how would you report the survey results on the percentage of supermarket shoppers who stock up on items when they find the item is a real bargain?

Report p̂.Report the confidence interval. Report p̂ along with the margin of error.Report the margin of error.

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

In a random sample of 64 professional actors, it was found that 41 were extroverts.

(a) Let *p* represent the proportion of all actors who are extroverts. Find a point estimate for *p*. (Round your answer to four decimal places.)

(b) Find a 95% confidence interval for *p*. (Round your answers to two decimal places.)

lower limit | |

upper limit |

Give a brief interpretation of the meaning of the confidence interval you have found.

We are 5% confident that the true proportion of actors who are extroverts falls within this interval.We are 5% confident that the true proportion of actors who are extroverts falls above this interval. We are 95% confident that the true proportion of actors who are extroverts falls within this interval.We are 95% confident that the true proportion of actors who are extroverts falls outside this interval.

(c) Do you think the conditions *np* > 5 and *nq* > 5 are satisfied in this problem? Explain why this would be an important consideration.

Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial.No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial. No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal.Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal.

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