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Stat 1222-011 (Professor: Dr. Biswas} Due: Tue 4/7/09
Name: ID#:
1. A maker of microwave ovens advertises that no more than 10% of its microwaves need repair during the
first five years of use. In a random sample of 57 microwaves five years old, 13% needed repairs. Test the
manufacturer’s claim. b . proportion WA love WAVE A
{a) State the null and the alte native hypotheses. veel: Anpuir>
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ai re Find the value of the standardized test statistic based on the observed sample. P >>-10
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EN. “rep t- sample propestion = 13 ne s 4.
n = 137 *h
z Basi 45 Se obgenvel Lo- F
level a = .06 and show the rejection rule. What is your decision at
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(c) Find the critical valué
2. A company manvfactures light bulbs. The company claims that the bulbs have a mean lifetime of 1000
hours. A random sample of 21 light bulbs is randomly selected and tested. The mean lifespan of the
sample is 1015 hours and the standard deviation is 25 hours. Assume that the distribution of lifetime of
light bulbs is normally distributed.
(a) State the null and the alternative hypotheses. € | aim’ Ma = woo
ve (MADD He APFIIOO 9 Fr00- tiled Oppy AF leo
(b) In the context of the problem, explain Type I error.
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tA true.
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{c) Find the value of the standardized test statistic based on the observed sample.
XK = 10s” < < = 1015 — toe
no 21, & 5, S=2td, be Bi = [019 ~ l000
ia wri
(d) Find the critical values at level a = .05 and show the rejection rule. State your decision. t = 2 . 45
Decision suds: Reject He if Ate n-\z 20.
Tet eg F< 2086 mtr rose Me -0F
= 106 ~ bo Decision > [ley eet Ho -
Thee is Leth LV duce Lb Hey eet H, (te cla»
