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 117 bars of Ivory soap. They find that 52 of them meet the 99.44% purity advertised.

Calculate the p-value.

Answer 1

p: Proportion of the bars of Ivory soap that are 99.44% pure (or more pure)

claim: at least half the bars of Ivory soap Proctor & Gamble produce are 99.44% pure i.e p0.50

Null hypothesis : Ho: p 0.50

Alternative hypothesis : Ha: p <0.50

Left tailed test.

Number of  bars of Ivory soap sampled : n= 117

Number of the sample met the 99.44% purity : x=52

Sample proportion of the bars of Ivory soap that are 99.44% pure : =52/117

Hypothesized proportion :po = 0.50

Test Statistic

For left tailed test :

p-value = 0.1145