10.12 A random sample of 400 voters in a certain city are asked if they favor an additional 4% gasoline sales tax to provide badly needed revenues for street repairs. If more than 220 but fewer than 260 favor the sales tax, we shall conclude that 60% of the voters are for it.
10.12 A random sample of 400 voters in a certain city are asked if they favor an additional 4% gasoline sales tax to provide badly needed revenues for street repairs. If more than 220 but fewer than 260 favor the sales tax, we shall conclude that 60% of the voters are for it.
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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Please answer question 10.13. Thank you in advance!
Transcribed Image Text:10.12 A random sample of 400 voters in a certain city are asked if they
favor an additional 4% gasoline sales tax to provide badly needed
revenues for street repairs. If more than 220 but fewer than 260 favor the
sales tax, we shall conclude that 60% of the voters are for it.
(a) Find the probability of committing a type I error if 60% of the
voters favor the increased tax..
(b) What is the probability of committing a type II error using this test
procedure if actually only 48% of the voters are in favor of the
additional gasoline tax?
10.13 Suppose, in Exercise 10.12, we conclude that 60% of the voters
favor the gasoline sales tax if more than 214 but fewer than 266 voters in
our sample favor it. Show that this new critical region results in a smaller
value for a at the expense of increasing B.
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