1 Fuel Efficiency Computers in some vehicles calculate various quantities related to performance. One of these is the fuel efficiency, or gas mileage, usually expressed as miles per gallon (mpg). A person conducted an experiment with his 2006 Toyota Highlander Hybrid by randomly recording mpg readings shown on the vehicle computer while the car was set to 60 mph by cruise control. Suppose the standard deviation of the population of mpg readings of this vehicle is known to be 6.5 mpg. What is the standard deviation of x ? Based on a 95% confidence level, what is the margin of error for the mean estimate? Given the margin of error computed, give a 95% confidence interval for , the mean highway mpg for this vehicle. The vehicle sticker information for the 2006 Toyota Highlander Hybrid states a highway average of 27 mpg. Are the results of this experiment consistent with the vehicle sticker? Clothing for runners Your company sells exercise clothing and equipment on the internet. To design the clothing, you collect data on the physical characteristics of your different types of customers. Data shows the weights (in kilograms) for a sample of 24 make runners. Assume that these runners can be viewed as a random sample of your potential male customers. Suppose also that the standard deviation of the population us known to be 4.5 kg. What is the standard deviation of x ? Give a 95% confidence interval for , the mean of the population from which the sample is drawn. Will the interval contain the weights of approximately 95% of similar runners? Explain your answer. Bottle Fill One of Bestea's most popular products is the 500 ml bottle of raspberry-flavored green tea. There is some variation from bottle to bottle because the filling machinery is not perfectly precise. Bestea has two concerns: whether there is a problem of underfilling (customers are then being shortchanged, which is the form of false advertising), or whether there is a problem of overfilling (unnecessary cost to the bottler). The filling process is not new to Bestea. Data on past production shows that the distribution of the contents is normal with standard deviation 2 ml. To assess the state of the bottling process, an inspector measures the contents of 10 randomly selected bottles. What is the mean content for this sample? Calculate the test statistic z. Determine the confidence intervals