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 149 bars of Ivory soap. They find that 68 of them meet the 99.44% purity advertised.

Calculate the p-value.

Answer 1

Claim :At least half the bars of Ivory soap they produce are 99.44% pure (or more pure) as advertised.

Here we have to test that

where

n = number of bars of Ivory soap selected randomly = 149

x = number of bars of Ivory soap meet the 99.44% purity advertised = 68

Sample proportion:

(Round to 4 decimal)

Test statistic:

z = -1.06 (Round to 2 decimal)

Test statistic = z = -1.06

P value:

Test is right tailed test.

P value= P(z > -1.06)

= 1 - P(z < -1.06)

= 1 - 0.1446 (From statistical table of negative z values)

= 0.8554

P value = 0.8554