10A few years ago, a cola manufacturer invited consumers to take a blind taste test. Consumers were asked to decide which of two sodas, Brand 1 or Brand 2, they preferred. The manufacturer was interested in determining what factors played a role in people's taste preferences. One of the factors studied was the age group of the consumer.

The table below summarises the findings:

Younger than 40 At least 40

Sample size 115 56

Number preferring Brand 1 50 20

Both samples were independently and randomly selected and each sample consists of identical independent trials. What requirements should be checked to ensure that the Normal approximation to the Binomial can be used when carrying out a hypothesis test for the difference in population proportions?

Select one:

a.

The population variances are known.

b.

Both sample sizes are greater than 30.

c.

For each of the two samples,np

^

10 andn(1p

^

)

10.

d.

The population variances are equal.