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1. A college football coach records the mean weight that his players can bench press as 280 pounds, with a standard deviation of 55 pounds . Three of his players thought that the mean weight was more than that amount. They asked 16 of their teammates for their estimated maximum lift on the bench press exercise. The data ranged from 205 pounds to 395 pounds. The actual different weights were: 205; 215; 225; 241; 252; 265; 275, 313; 316; 338; 341; 345; 368; 375; 388; 395. Conduct a hypothesis test using a 8% level of significance to determine if the bench press mean is more than 280 pounds. n=16 X total BS - D. 02 16 p - 280 5 0 - 55 From the given data, we have: S = 1 EX - X )2 n - 16, sample mean - 303, 56 5 sample S. D. - 54.24 n -1 Step 1: Set up the Hypothesis Test: Since the problem is about the mean weight, this is a test of a single population mean. Ho: w = 280 B.: p > 280 (more than) > this is right-tailed test Step 2: Determine the distribution needed: Random variable: X = the mean weight, in pounds, lifted by the football players Distribution for the test: Normal Distribution (Z-Diat.) since a is known > N(p - 280, ox - 55/sqrt [16) ] where o - 55 Step 3: Calculate the p-value: p-value P (x > 303 . 56) - P(z > (303.56-280]/(55/=qet (16) .1 - P(z > 1.7133) 4.36% - 1 - 0. 9564 (from Z-Table) 1= 280 - 0, 0436 - 4.364 303% X Interpretation of the p-value: If H, is true, then there is a 4.361 probability that the football players can lift a mean weight of 303.56 pounds or more. Step 4: Compare a and the p-value: > a = 84 > p-value = 4.369 Make a Decision: Reject Ho (Accept H.) Step 5: Write a Conclusion: At the 8\\ level of significance, from the sample data, there is sufficient evidence to conclude that the true mean weight lifted is more than 280 pounds. 2. Emma's Extreme Sports hires hang-gliding instructors and pays them a fee of $80 per class as well as $25 per student in the class. The total cost Emma pays depends on the number of students in a class. a. Find- the equation, y - a + bx, that expresses the total cost in terms of the number of students in a class. y - 80 + 25x b. What are the independent and dependent variables? independent variable " x - # of students and dependent variable - y - total cost c. What is the y-intercept and what is the slope? Interpret them using complete sentences. y-intercept - (0, 80) and the slope - 25 d. How much does Emma pay for a class with 16 students? y - 80 + 25 (16) - $480 e. How many students are there if Enma needs to pay a total cost of $1, 0807 2, 080 - 80 + 25x students