Question

1. 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 Gamble's competitors, wishes to put this claim to the test. They sample the purity of 123 bars of Ivory soap. They find that 52 of them meet the 99.44% purity advertised

Calculate the p-value. Round to 4 decimal places.

2. Given ˆpp^ = 0.2857 and N = 35 for the high income group,

Test the claim that the proportion of children in the high income group that drew the nickel too large is smaller than 50%. Test at the 0.05 significance level.

a) The test statistic value is:   

b) Using the P-value method, the P-value is:

3.

For a confidence level of 90% with a sample size of 22, find the critical t value. Round your answer to 3 decimal places.

Answer 1

We would be looking at the first question hypothesis test here.

As we are testing here whether at least half the bars of Ivory soap they produce are 99.44% pure, therefore the null and the alternative hypothesis here are given as:

the sample proportion here is computed as:
p = x/n = 52/123 = 0.4228

The test statistic here is computed as:

As this is a one tailed test, the p-value here is obtained from the standard normal tables as:
p = P(Z <-1.71) = 0.0436

Therefore 0.0436 is the required p-value here.