Question

Suppose the 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

Construct a 95% confidence interval for the population proportion of households where the women make the majority
of the purchasing decisions. State the confidence interval, sketch the graph and calculate the error bound.

Answer 1

The sample proportion here is computed as:
p = x/n = 120/200 = 0.6

From standard normal tables, we have here:
P( -1.96 < Z < 1.96) = 0.95

Therefore the confidence interval here is obtained as:

This is the required 99% confidence interval for the population proportion of households where the women make the majority

This is given in the graph as: