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Lecture 11

# Lecture 11 - Z Tests Two-Tail Tests With a two tail test...

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Z Tests Two-Tail Tests: With a two tail test, the α error is split into two with α /2 going into each tail. EXAMPLE: A manufacturer produces bolts with a thickness of exactly 1inch (purportedly). A customer takes a random sample of 100 bolts and find that =1.2 inches and s = .40 inches. Should the manufacturer’s claim, that the bolts are exactly 1 inch (on average) be rejected? Test at α = 0.01. H 0 : μ = 1.00 inch H 1 : μ 1.00 inch Therefore, reject H 0 at P < .01 Let’s try this as a 99%, Confidence Interval Estimator 1.20 ± 2.575 (0.04) = 1.20 ± .103 1.097 ——— 1.303 inches [NOTE: 1.00 is NOT in this interval!]

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EXAMPLE: A toothpick manufacturer wants every box to contain exactly (on average) 500 toothpicks. Suppose you took a random sample of n = 81 boxes, and found: =498 toothpicks S = 9 toothpicks Test at α = .10 H 0 : μ = 500 H 1 : μ 500 REJECT H 0 Therefore, we reject H 0 at p < .1 As a 90%, Confidence Interval: 498 ± 1.645 = 498 ± 1.645(1) 496.36 ——— 499.65 toothpicks per box
[REJECT H 0 : 500 is NOT in the interval]EXAMPLE: A researcher claims that 10 year olds watch 6.6 hours of TV daily. You try to verify this with the following sample data.

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Lecture 11 - Z Tests Two-Tail Tests With a two tail test...

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