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A random sample of thirty firms dealing in wireless products was selected to determine the proportion of such firms that have implemented new software to improve productivity. It turned out that eight of the thirty have implemented such software. Compute a 95% confidence interval on p, the true proportion of such firms that have implemented new software. In other situation, suppose there is concern about whether or not the point estimate of p = 8/30 is accurate enough because the confidence interval around p is not sufficiently narrow. By using p as your estimate of p, calculate how many companies would need to be sampled to have a 95% confidence interval with a width of only 0.05. (10 marks)
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