1. Sales team of a New Ventures Company is in the process of introducing a new product. As an initial step company conducted a survey of prospective customers. Estimate how large a sample should company take if they want to estimate the proportion of people who will buy the product to within 3%, with 99% confidence.
2. A researcher has taken a random sample of 8 observation from a normal population. Sample mean and standard deviations are 75 and 50 respectively. Using the 6 steps process of hypothesis testing.
   1. Can he infer at the 10% significance level that the population mean is less than 100?
   2. Can he infer at the 10% significance level that the population mean is less than 100 if population standard deviation is 50?
   3. Review the answers in (i) and (ii) and explain why the test statistics differed.