Name _________________________________Two Sample Inference Project & Review20 points Due: April 8, 20141. MacDonald’s executives want to experiment with redesigning its restaurants so that thecustomers form one line leading to four registers, rather than four lines leading to four separate registers. They redesign randomly selected restaurants with the single line. In addition, they randomly select restaurants with the four line configuration to participate in the study. At each restaurant, an employee monitors the wait time (in minutes) of randomly selected patrons. Use the data below to test if the standard deviation for the wait time in the single line is less than the standard deviation of wait time in the multiple lines at the 0.0 5 level of significance. (3 points)Single Line Multiple Lines 1.2 2.1 1.7 2.8 1.1 1.6 2.9 4.61.9 2.1 2.4 3.0 3.8 2.9 2.8 2.92.1 2.3 1.9 2.9 4.3 2.3 2.0 2.62.7 2.0 2.9 2.3 1.3 1.3 2.0 2.72.8 1.1 3.1 1.8 2.0 3.2 2.3 0.92. Next test the equality of the mean wait time for the two different methods of providing service to determine if the average wait time is less for the multiple line method. Use the 0.05 level of significance. (3 points)3. Write a conclusion about the answers for questions 1 and 2. ( 1 point)4-6. The aluminum bottle first introduced in 1991 for mainly personal and household items like lotions has become popular with beverage companies. Besides being light weight, the aluminum bottle is reported to cool faster and stay cold longer than glass bottles. The data below is used to analyze the bottle choices.Bottle type Sample Size Mean St Dev Glass 42 133.8 min 9.9Aluminum 35 92.4 min 7.3a. Use the data above and construct a 95% confidence interval for the difference between the mean scores for glass and aluminum bottles. (1 points)b. Use the data above and construct a 95% confidence interval estimate for the mean timefor aluminum bottles. (1 point)c. Construct a 90% confidence interval estimate for the variance in the mean flexibility score for all aluminum bottles. (1 point)7. A Secchi disk is an 8-in diameter weighted disk that is painted black and white and attached to a rope. The disk is lowered into the water and the depth (in inches) at which itis no longer visible is recorded. The measurement is an indication of water clarity. An environmental biologist is interested in determining whether the water clarity of the lake at Joliet Junior College is improving. She takes measurements at the same location on thesame dates during the course of a year and repeats the measurements 5 years later. The results follow:Date 5/11 6/7 6/24 7/8 7/27 8/31 9/30 10/12 Initial Depth 38 58 65 74 56 36 56 52 Depth 5 years later 52 60 72 72 54 48 58 60 Test at the 0.01 level of significance. (2 points)8. Accupril is a medication supplied by Pfizer Pharmaceuticals, is meant to control hypertension. In clinical trials of Accupril, 2142 subjects were divided into two groups. The 1563 patients in Group 1 received Accupril (experimental group) and 579 patients in Group 2 received a placebo. Of the 1562 Group I patients, 61 reported dizziness. 15 patients in the control group (placebo group) experienced dizziness. Use the 0.05 level of significance to test that a greater percent of patients in the experimental group experiencing dizziness than in the control group. (2 points)9. Z is a standard normal random variable. Find each probability (3 points)P (z > 1.45) = ________________ P (-1.85 < z < 2.46) = ________________P (z < 2.45) = _______________ P (z = 2.45) = ______________________P (z > 129) = ________________ P z < 14.5) = _______________________10. If 40% of the students at Berks have attended a Penn State football game, what is the chance that (3 points)a. exactly 6 of the next15 student will have attended a football game?b. at least 5 of the next randomly selected sample of 10 students will have attended a game?b. 8 or fewer of the next randomly selected sample of 20 students will have attended a