Estimating p In Binomial Dist Worksheet Answers

  1. Consider binomial trials with successes.

a)Is it appropriate to use a normal distribution to approximate the distribution?

Yes, both are > 5

b)Find a 95% confidence interval for the population proportion of successes

  1. What is the minimal sample size needed for a 95% confidence interval to have a maximal margin of error of 0.1

a)If a preliminary estimate for

round up to 73

b)If there is no preliminary estimate for

round up to 97

  1. Isabel Myers was a pioneer in the study of personality types. In a random sample of 62 professional actors, it was found that 39 were extroverts.

a)Let represent the proportion of all actors who are extroverts. Find a point estimate for

b)Find a 95% confidence interval for

  1. Case studies showed that out of 10,351 convicts who escaped from U.S. prisons, only 7867 were recaptured.

a)Let represent the proportion of all escaped convicts who will eventually be recaptured. Find a point estimate for

b)Find a 99% confidence interval for

  1. In a marketing survey, a random sample of 1001 supermarket shoppers revealed that 273 always stock up on an item when they find that item at a real bargain price.

a)Let 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

b) Find a 95% confidence interval for

  1. In a survey of 1000 large corporations, 250 said that, given a choice between a job candidate who smokes and an equally qualified nonsmoker, the nonsmoker would get the job.

a)Let represent the proportion of all corporations preferring a nonsmoking candidate. Find a point estimate for

b)Find a 0.95 confidence interval for

  1. How difficult is it to reach a business person by phone ? Let 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 , how many business phone calls should you include in a random sample to be 80% sure that the point estimate will be within a distance of 0.03 from ?

** Rounded to 456

b)What is studies have shown that businesspeople can be reached by a single phone call 17% of the time. What sample size is needed for an 80% success rate for within a distance of 0.03 from ?

** round to 257

  1. What percentage of college campuses are female ? Let be the proportion of women students on a college campus.

a)If no preliminary study is made to estimate how large a sample is needed to be 99% sure that a point estimate will be within a distance of 0.05 from ?


round to 662the meaning of th0.51er part a) with this new informatione phone call 17% of the time. what an 80%ry.
ker, the no

** round to 666

b)If there is a study showing that 54% of college students are female, answer part (a) with this new information

c)

** round to 662