Final answer:
Based on a sample of 200 households where women made the majority of purchasing decisions in 120 of them, the estimated population proportion is 60% (P' = 0.6). This is the sample's estimation of the percentage of households where women are the primary decision-makers in purchases.
Step-by-step explanation:
The population proportion of households where women make the majority of the purchasing decisions can be estimated using the sample proportion from the surveyed data. In the survey conducted by the marketing company, they found that out of 200 randomly surveyed households, 120 had women making the majority of purchasing decisions. To determine the population proportion (P'), we would use the formula P' = X/n, where X is the number of successes, and n is the total number of trials.
In this case, X = 120 and n = 200. Therefore, the estimated population proportion P' is calculated as 120/200, which simplifies to 0.6 or 60%. This means that, based on the sample, it is estimated that 60% of the households have women making the majority of purchasing decisions. However, this is an estimate from the sample and may not be the exact population proportion.
To better understand the population proportion, researchers might construct a confidence interval or conduct further sampling. Also, note that while this estimate suggests a trend, factors like the method of surveying and the potential for response bias should be considered when generalizing to the entire population.