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Recently a survey was conducted to assess the quality of investment brokers. A random sample of 6 brokerage houses was selected from a total of 27 brokerage houses. Each of the brokers in the selected brokerage houses was evaluated by an independent panel of industry experts as “highly qualified” (HQ) or was given an evaluation below this rating. The designers of the survey wanted to estimate the proportion of all brokers in the entire industry who would be considered highly qualified. The survey results are in the following table.
Use the cluster sampling estimator of the population proportion to estimate the proportion of all highly qualified brokers in the investment industry. Also give a 99% confidence interval for the population proportion you estimated.