Suppose that Sam, owner of a large fitness center franchise in a metropolitan area, wants to assess customer satisfaction among fitness center members. Sam wants to estimate the difference in the proportion of male members that are satisfied and the proportion of female members that are satisfied. Sam randomly selects 15 male members and 8 female members and conducts a phone survey to determine whether or not each individual is satisfied with their membership offerings. He finds that 13 men are satisfied and 7 women are satisfied. Sam plans to use this data to develop a plus-four 90% confidence interval for the difference of the proportion of satisfied male members and the proportion of satisfied female members. Select the statement that accurately evaluates whether or not a plus-four confidence interval for two proportions is appropriate for Sam's analysis. A.plus-four confidence interval for two proportions is appropriate because the samples are simple random samples taken from large populations and the variable of interest is categorical with a success or failure outcome. B.A plus-four confidence interval for two proportions is not appropriate because the sample sizes are too small and the confidence level for the constructed confidence interval is not 95% C.A plus-four confidence interval for two proportions is appropriate because the samples are simple random samples taken from large populations and the number of successes for the categorical variable in each sample is large enoughD.A plus-four confidence interval for two proportions is not appropriate, despite the random selection of two independent samples, because there are not enough successes and failures in the samples. E.A plus-four confidence interval for two proportions is appropriate because the samples are of adequate size, are randomly selected from large populations, and the variable in the population is categorical with two possible outcomes.
