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Type 2 error, 2 questions

  1. Mar 11, 2010 #1
    1) A car producer claims a certain type of car is fuel-saving and can be driven 25 miles/gallon and a st dev of 2.8 miles/gallon.
    An analyst wants to test this claim and wants a 1% risk of concluding the statement is false when it in fact is true. He chooses 30 observations.

    Calculate the probability for type 2 error if the true mean is 24?

    I tried:
    X-bar critical = 26.32 and 23.68 and got P(-0.62 < Z < 4.53) = F(0.62)

    But the book's answer is 0.64?


    2)
    A company considers launching a new product if the proportion of customers who will buy it is at least 0.2.
    A sample of 100 was taken. The null hypothesis (P =0.2) is rejected if the smaple proprtion is at least o.27.

    The following requirements must be met:
    P(not rejecting H0) = at least 99% if true proportion is 0.17
    P(rejecting H0) = at least 99% if true proportion is 0.27

    e) What sample size is required (at least)?
    Book: 365
    f) What is the significance level?
    Book: 17%

    How do you solve this??
     
  2. jcsd
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