Results 1 to 2 of 2

Math Help - Stats: Creating confidence interval

  1. #1
    Newbie
    Joined
    Nov 2006
    Posts
    15

    Stats: Creating confidence interval

    mm
    Last edited by chillerbros17; February 28th 2007 at 02:27 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by chillerbros17 View Post
    Direct mail advertisers send solicitations to thousands of potential customers in the hope that some will buy the company's product. The rsponse rate is usually quite low. Suppose a company wants to test the response to a new flyer, and sends it to 1000 people randomly selected fromtheir mailing list of over 200,000 people. THey get orders from 123 of the recipients.

    a) Create a 90% confidence interval for the percentage of people the company contacts who may buy something.
    The number of respondents to test mailing of 1000 is 123, both these
    numbers are large enough that we may assume that the Normal
    approximation to the Binomial distribution is appropriate.

    Then (N is the sample size in this case 1000, and p is the proportion of
    recipients that will respond):

    z = [123 - pN]/sqrt[N p (1-p)]

    has a standard normal distribution, and so in 90% of cases lies between
    +/-1.645. So:

    -1.645 < [123 - pN]/sqrt[N p (1-p)] < 1.645

    90% of the time, rearranging these inequalities:

    -1.645 sqrt[N p (1-p)] < 123 -pN < 1.645 sqrt[N p (1-p)]

    or:

    [123-1.645 sqrt[N p (1-p)]]/N < p < [123+1.645 sqrt[N p (1-p)]]/N

    90% of the time.

    The problem now is that we don't know the value of sqrt[N p (1-p)], so
    we have to estimate it from out test sample, for which N=1000, and our
    estimate for p is pest=123/1000=0.123. In which case our estimate of
    sqrt[N p (1-p)] is 10.39, and our inequality is now:

    [123-1.645*10.39]/1000 < p < [123+1.645*10.39]/1000,

    or:

    0.106 < p < 0.140.

    Which gives a 90% confidence interval for p of approximately (0.106, 0.140).



    b) Explain what this interval means.
    This interval is a random variable which 90% of the time contains the
    actual proportion of respondents.

    c) Explain what "90% confidence" means.
    see above

    d) The company must decide whether to now do a mass mailing. The mailing won't be cost-effective unless it produces at least 5% return. What does your confidence interval suggest? Explain.
    The confidence interval suggests that the results obtained from the test
    shot are unlikely to have been the result of a test on a population with a
    response rate as low as 5%, but only suggests this as this is the wrong
    procedure to apply for this last part.

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Confidence Interval Mean
    Posted in the Statistics Forum
    Replies: 1
    Last Post: June 8th 2011, 03:41 AM
  2. stats: confidence interval
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: March 3rd 2011, 03:00 PM
  3. confidence level and confidence interval?
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: July 12th 2009, 06:59 AM
  4. stats: Confidence Interval!
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: July 26th 2008, 03:00 AM
  5. confidence interval
    Posted in the Statistics Forum
    Replies: 1
    Last Post: July 30th 2007, 09:08 PM

Search Tags


/mathhelpforum @mathhelpforum