Question

Marketing companies are interested in knowing the population percent of women who make the majority of household purchasing decisions.

Suppose a marketing company did do a survey. They randomly surveyed 200 households and found that in 120 of them, the woman made the majority of the purchasing decisions. We are interested in the population proportion of households where women make the majority of the purchasing decisions.

Which distribution should you use for this problem and why?

p'~_(_,_)

Answer 1

It's a problem related to Population Proportion

In this, p′ = x / n where x represents the number of successes and n represents the sample size. The variable p′ is the sample proportion and serves as the point estimate for the true population proportion. q′ = 1 – p′

The variable p′ has a binomial distribution that can be approximated by the normal distribution

here, X is the number of “successes” where the woman makes the majority of the purchasing decisions for the household. P′ is the percentage of households sampled where the woman makes the majority of the purchasing decisions for the household.

x = 120
n = 200
p′ = 0.6

Distribution should be used as