A consulting company has developed a short course on modern business forecasting methods for corporate executives. The first course was attended by 150 executives. From the information they supplied, it was concluded that the technical skills of 100 course members were more than adequate to follow the course material, whereas those of the remaining 50 were judged barely adequate. After the completion of the course, questionnaires were sent to independent random samples of 25 people from each of these two groups in order to obtain feedback that could lead to improved presentation in subsequent courses. Six of the more skilled group and 14 of the less skilled group indicated that they believed the course had been too theoretical.
a. Find an estimate of the proportion of all course members with this opinion, using an unbiased estimation procedure.
b. Find 90% and 95% confidence intervals for this population proportion.