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

Question

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 106 bars of Ivory soap. They find that 48 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 right-tailed test two-tailed test Calculate the p-value. Does Unilever have sufficient evidence to reject Proctor& Gamble's claim? Yes No

Explanation / Answer

1.

If the sample size is more than 30 then the Z test can be used.

2.

Therefore, Z-test of a proportion should be used.

3

The question says that we have test the claim if it is greater than half. So, the hypothesis is facing rightwards
Hence, it is a right tailed test

4.
p-value = ?
Lets calculate Z statistic first = ?
Z = (p^-p)/sqrt(p*p'/n). p^ = 48/106 = .453, p0 = .50
So, Z = (.453-.50)/sqrt(.5*.5/106) = .97
So,p-value corresponding to this Z statistic is .1660

5.

No. Since the p-value is much more than .05, Unilever doesn't have sufficient eveidence to reject P & G' claim.
Answer is NO

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