Final answer:
This question pertains to statistics within Mathematics, specifically binomial distributions and constructing confidence intervals. College students learning about these topics will identify random variables X and P', use binomial distribution, and construct a 95% confidence interval for a population proportion.
Step-by-step explanation:
The subject of this question is Mathematics, specifically statistics and probability as it relates to constructing confidence intervals and understanding random variables and distributions. The question appears to be geared towards college students who are studying these concepts in their coursework.
Identify the following:
- a. X = 15 (the number of success or favorable outcomes)
- b. n = 54 (the total number of trials or sample size)
- c. p' = 15/54 ≈ 0.278 (the sample proportion)
The random variables X and P' can be defined as follows:
- X is the number of households where women make the majority of purchasing decisions in a sample of households.
- P' is the proportion of households in the sample where women make the majority of purchasing decisions.
To solve this problem, we should use the binomial distribution as it pertains to discrete outcomes in statistically independent trials.
We can construct a 95 percent confidence interval for the population proportion using the sample proportion (p') and the sample size (n). We also make use of the standard normal distribution since the sample size is large enough. The error bound is calculated using the standard error of the proportion.