Proctor & Gamble claims that at least half the bare of Ivory soap they produce a

Question

Proctor & Gamble claims that at least half the bare of Ivory soap they produce arc 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 125 bars of Ivory soap. They find that 53 of them meet the 99.44% purity advertised. What type of test should be run? z-test of a proportion t-test of a mean The alternative hypothesis indicates a left-tailed test two-tailed test right-tailed test Calculate the p-value. Does Unilever have sufficient evidence to reject Proctor Sc Gamble's claim? Yes No

Explanation / Answer

This is a z test of a proportion

The alternative hypothesis indicates a left tailed test

z = (p - P)/sqrt(P*(1-P)/n) = [53/125 - 0.5]/sqrt((0.5*0.5)/125) = -1.699, p = 0.0446

As p < 0.05, yes, there is sufficient evidence to reject

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