SOLUTION: Proctor & Gamble claims that at least half the bars of Ivory soap they produce are 99.44% pure (or more pure) as advertised. Unilever, one of Proctor & Gamble's competitors, wishes

Question 1133557: Proctor & Gamble claims that at least half the bars of Ivory soap they produce are 99.44% pure (or more pure) as advertised. Unilever, one of Proctor & Gamble's competitors, wishes to put this claim to the test. They sample the purity of 112 bars of Ivory soap. They find that 44 of them meet the 99.44% purity advertised.
1. Multiple choice: What type of test should be run?
(a) t-test of a mean
(b) z-test of a proportion

2. Multiple choice: The alternative hypothesis indicates a
(a) right-tailed test
(b) two-tailed test
(c) left-tailed test

3. Calculate the p-value: __________

4. Multiple choice: Does Unilever have sufficient evidence to reject Proctor & Gamble's claim?
(a) Yes
(b) No
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
This is a one sample proportion test
Ho: purity is in 0.5 of them or more
Ha: purity is not in 0.5 of them
left tailed test with 5% (if this is desired) at z<=-1.645
44/112 is 0.393
z=(0.393-0.5)/sqrt (0.393*0.607/112)
=-.107/0.0462
=-2.32
p=0.010
Yes, there is sufficient evidence to reject the claim even at the 1% level.

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