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 131 bars of Ivory soap. They find that 52 of them meet the 99.44% purity advertised. What type of test should be run? t-test of a mean z-test of a proportion The alternative hypothesis indicates a two-tailed test right-tailed test left-tailed test Calculate the p-value. Does Unilever have sufficient evidence to reject Proctor & Gamble's claim? No Yes

Answer 1

z-test of a proportion.

The alternative hypothesis indicates a left-tailed test.

p = 52/131 = 0.4

The test statistic z = (p - P)/sqrt(P(1 - P)/n)

                              = (0.4 - 0.5)sqrt(0.5 * 0.5/131)

                              = -0.004

P-value = P(Z < -0.004)

             = 0.4980

At 5% significance level as the P-value is greater than the significance level (0.4980 > 0.05), we should not reject the null hypothesis.

No Unilever does not have sufficient evidence to reject Proctor and Gamble's claim.