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 105 bars of Ivory soap. They find that 49 of them meet the 99.44% purity advertised. What type of test should be run? Ot-test of a mean Oz-test of a proportion The alternative hypothesis indicates a O two-tailed test O left-tailed test Oright-tailed test Calculate the p-value. Does Unilever have sufficient evidence to reject Proctor & Gamble's claim? O No Yes

Answer 1

n = 105 X = 49 P-0.5 q=0.05 0:47 ܘ> - Х h 49 105 W z Jest of a proportion >> The null and cellenctive hypothesis are Ho: P. 20.5 Ha: P = 0·5 ( Right-tailed Jest) → Z test statistic :- Z - P-P 0.47-0.5 P(1-P) 0.5 (1-0.5) m 105 Z - -0.61 Po value pl Z Z Zrest ) PqZ Z -0.61 ) 1-P122-0.61) = 0.2793 0-2.793 ( using 2-table - 1 0.2793 0.7207 P-value we Since (P- value>d), fail to Reject Ho. Yes] Unikver have sufficient evidence to Reject Proctor & Gamble's claim.