Exercise 1. (2 points) The following measurements of the drying time, in hours, of a certain brand of vinyl paint are recorded: 3.4 2.5 4.8 2.9 3.6 2.8 3.3 5.6 3.7 2.8 4.4 4.0 5.2 3.0 4.8 Assume that the measurements represent a random sample from a normal population, and based on this, calculate the 95% prediction interval for the drying time of the following paint test.Exercise 2. [3 points) The National Weight Control Registryr tries to get success secrets from people who have lost at least 3|] pounds and kept the weight off for at least a year. The agency reports that of 2300 registered, 459 were on a low-carbohydrate diet {less than 90 grams a day]. a. Construct the 95% confidence interval for this fraction. b.15 it possible that the percentage of the population is 18 percent? c. How large does the sample need to he to estimate the proportion to within I15 percent? Exercise 3. [5 points} Today, most air travelers buy their tickets online. In this way, passengers avoid the worry of taking care ofa paper ticket. in addition to saving airlines. Recently, however, airlines have received complaints related to tickets, particularly when a link is required to change lines. To analyze the problem, an independent research agency sampled 20 airports and collected information related to the number of complaints about tickets during May. The information is presented below. \"mm -\"--n- At the CLUE level of signicance. can the investigating agency conclude that the mean number of complaints per airport is less than '15 per month? Exercise 4. (5 points) In most sports it is customary to toss a coin to decide which team gets the ball first. This requires little effort and is believed to give both teams an equal chance. In 43 Super Bowl games, the National Football Conference has won these tosses 29 times, while the American Football Conference has only won 14 times. Do a hypothesis test at the 0.01 level of significance to test whether these data suggest that it is fair to flip the coin. Also calculate the p-value.Exercise 5. (5 points) The following table lists the price of 12 randomly selected laptops, along with their corresponding processor speeds in gigahertz. Computer Speed Price Computer Speed Price 2.0 $2017 7 2.0 $2197 two 1.6 922 8 1.6 1387 1.6 1064 9 2.0 2114 1.8 1942 10 1.6 2002 2.0 2137 1.0 937 6 1.2 1012 12 1.4 869 a) Make a velocity-price scatter plot and indicate the behavior of these data. b) Indicate which is the dependent variable and which is the independent variable. c) Write a linear regression equation for these data. d) What would be the speed of a computer if its price were $2600. e) Calculate the coefficient of determination and interpret it