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Q.2 In a random sample of 361 owners of small businesses that had gone into bankruptcy, 105 reported conducting no marketing studies prior to opening the business. Test the hypothesis that at most 25% of all members of this population conducted no marketing studies before opening their businesses. Use a = 0.05.
Q.3 The production manager of Circuits Unlimited has asked for your assistance in analyzing a production process. This process involves drilling holes whose diameters are normally distributed with a population mean of 2 inches (consider as null hypothesis) and standard deviation of 0.06 inch. A random sample of nine measurements had a sample mean of 1.95 inches. Use a significance level of a = 0.05 to determine if the observed sample mean is unusual and, therefore, that the drilling machine should be adjusted.
Q.4 An IT consultancy in Singapore that offers telephony solutions to small businesses claims that its new call-handling software will enable clients to increase successful inbound calls by an average of 75 calls per week. For a random sample of 25 small-business users of this software, the average increase in successful inbound calls was 70.2 and the sample standard deviation was 8.4 calls. Test, at the 5% level, the null hypothesis that the population mean increase is at least 75 calls.