Sampling Distribution of the Sample Mean An orange juice producer buys all his oranges from a large orange grove that has one variety of orange. The amount of juice squeezed from these oranges has a mean of 4.70 ounces and a standard deviation of 0.60 ounces. After an early frost, the producer is concerned that the quality of the oranges has been compromised and that the amount of juice squeezed from each orange will decrease. A random sample of 45 oranges from the latest shipment is selected, and the average amount of juice squeezed from the sample of oranges is recorded. Identify what variable was recorded in this example. Is it a qualitative or quantitative variable? What conjecture has been made by the producer? Assuming the amount of juice squeezed from these oranges has not been affected by the early frost, completely describe the sample mean amount of juice squeezed from a sample of 45 oranges. The sample of 45 oranges had an average 4.62 ounces of juice. Assuming the early frost has not affected juice amounts, what is the probability of observing a sample mean of 4.62 ounces or less? Based on the probability found above, what (if anything) can be inferred about the mean amount of juice squeezed from the oranges after the early frost?In 2008, Barron's reported that the mean length of time an individual is unemployed after losing their job is 17.5 weeks with a standard deviation of 4 weeks. At that time, the distribution of the length of unemployment was strongly positively skewed (right-skewed). Given the current economic crisis, what conjecture would you make about the mean length of time someone is unemployed after losing their job in 2011? If a sample of 15 individuals who lost their job but subsequently found employment is taken, how would the sampling distribution of the sample mean length of unemployment time be described? If a sample of 35 individuals who lost their job but subsequently found employment is taken, how would the sampling distribution of the sample mean length of unemployment time be described? Suppose that a sample of 35 individuals is taken, and they report a sample mean unemployment length of 19.6 weeks. If we assume that the true mean length of unemployment time for all individuals remains 17.5 weeks, what is the probability of observing a sample mean length of 19.6 weeks or longer? Based on the probability above, what (if anything) can be inferred about the mean length of unemployment time in 2011