ESSENTIALS OF STATISTICS FINAL-EXAM Instruction: performed. a) b) c) d) Use the following steps of hypothesis testing whenever a test is to be Identify the claim state the hypothesis Compute the test value Determine either the P-value or the critical values (indicating the degrees of freedom when necessary) e) Make a decision f) Draw a conclusion or provide an answer to the question. Exercise 1 2.5 points 1. A small electronics store has begun to advertise in the local newspaper. Before advertising, the long-term average weekly sales were $9,820. A random sample of 50 weeks while the newspaper ads were running gave a sample mean weekly sales of = x $10,960. Does this indicate that the population mean weekly sales is now more than $9,820? Test at the 5% level of significance. Assume = $1,580 1 2. The owner of Prices Limited claims that 75% of all the items in the store cost less than $5. Suppose that you check a random sample of 146 items in the store and find that 105 cost less than $5. Does this indicate that the proportion of items in the store that cost less than $5 is different from 75%? Use = 0.01. 2 Exercise 2 2.5 points 1. A new bus route has been established between downtown Denver and Englewood (a suburb of Denver). Dan has taken the bus to work for many years. For the old bus route, he knows from long experience that the mean waiting time between buses at his stop was = 20 minutes. However, a random sample of five waiting times between buses using the new route had mean = 15.1 minutes with sample x standard deviation s = 6.2 minutes. Does this indicate that the population mean waiting time for the new route is shorter than what it used to be? Use = 0.05. Assume that x is normally distributed. 2. Five members of the college track team in Denver (elevation 5,200 feet) went up to Leadville (elevation 10,152 feet) for a track meet. The times in minutes for these team members to run 2 miles at each location are shown below Team member Denver Leadville Ojai 10. 7 11.5 Edgar 9.1 10.6 Euclid 11.4 11.0 Seymou r 9.7 11.2 Sylvia 9.2 10.3 Assume that the team members constitute a random sample of track team members. Use a 5% level of significance to test the claim that the times were longer at the higher elevation 3 Exercise 3 2.5 points 1.Students at the college agricultural research station are studying egg production of free-range chickens compared with caged chickens. During a 1-week period, a random sample of n1 = 93 free-range hens produced an average of = 11.2 eggs per 1 hen. For the same period, another random sample of n2 = 87 caged xhens produced a sample average of = 8.5 eggs per hen. Previous studies show that and x2 indicate the population mean egg production for 1 free-range 4.4 eggs Does this 2 5.7 eggs. hens is higher? Use a 5% level of significance. 4 2.Two models of a popular pickup truck are tested for miles per gallon (mpg) gasoline consumption. The Pacer model was tested using a random sample of n1 = 9 trucks, and the sample mean was = 27.3 mpg with sample standard deviation s1 = 6.2 x1 was tested using a random sample of n2 = 14 trucks. mpg. The Road Runner model The sample mean was = 22.5 mpg with sample standard deviation s2 = 6.8 mpg. x2 population mean gasoline consumption for the Pacer is Does this indicate that the higher than that of the Road Runner? Use = 0.01. 5 Exercise 4 2.5 points 3. A telemarketer is trying two different sales pitches to sell a carpet cleaning service. For his aggressive sales pitch, 175 people were contacted by phone, and 62 of those people bought the cleaning service. For his passive sales pitch, 154 people were contacted by phone, and 45 of those people bought the cleaning service. Does this indicate that there is any difference in the population proportions of people who will buy the cleaning service depending on which sales pitch is used? Use = 0.05. 4. a) b) c) d) Physicians have used the \"diving reflex\" to reduce abnormally rapid heartbeats in humans by briefly submerging the patient's face in cold water. The reflex, triggered by cold water temperatures, is an involuntary neural response that shuts off circulation to the skin, muscles, and internal organs to divert extra oxygen-carrying blood to the heart, lungs, and brain. A research physician conducted an experiment to investigate the effects of various cold water temperatures on the pulse rate of small children. The data for seven 6-year-old children are shown. Temperature of Water x Decrease in Pulse Rate y 68 2 65 5 70 1 62 10 60 9 55 13 58 10 What is the correlation coefficient Is there a significant correlation between the temperature of water x and the Decrease in pulse rate at 1% significance level? What is the regression line? If the water temperature is 65 F , predict the drop in pulse rate for a 6-year-old child. 6 e) What is the standard error of estimate of this prediction? f) What proportion of variation of the decrease in pulse rate can be explained by the regression line and the temperature of water? g) What are the coefficient of non-determination of this correlation? 7