Question 1

A PE teacher believes that his year 12 cohort can run 500 meters in exactly 130 seconds. To test if this belief is correct, a sample of 100 randomly selected students is drawn and the time recorded. The sample mean of this is 126.8 seconds. If the running time is normally distributed with a standard deviation of 15 seconds, can we conclude that the belief regarding the mean is incorrect? (Assume Alpha = 0.05)

Question 2

After careful analysis, a company contemplating the introduction of a new product has determined that it must capture a market share of 5% to break even. Anything greater than 5% will result in a profit for the company. In a survey, 800 potential customers are asked whether or not they would purchase the product and their responses were recorded, if 104 people respond affirmatively, is this enough evidence to enable the company to conclude that the product will produce a profit? (Use a 95% significance level)