2-3 Assignment Hypothesis Testing Using Minitab

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Southern New Hampshire University *

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Jan 9, 2024

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2-3 Assignment: Hypothesis Testing Using Minitab® By Laura Turgeon December 17, 2023 QSO-620 Six Sigma Quality Management Professor: Thomas Timmins
Problem 1 Jeffrey, as an eight-year-old, established an average time of 16.43 seconds for swimming the 25-yard freestyle, with a standard deviation of 0.8 seconds. His dad, Frank, thought that Jeffrey could swim the 25-yard freestyle faster by using goggles. Frank bought Jeffrey a new pair of expensive goggles and timed Jeffrey for 15 25-yard freestyle swims. For the 15 swims, Jeffrey's average time was 16 seconds. Frank thought that the goggles helped Jeffrey to swim faster than the 16.43 seconds. Conduct a hypothesis test using a preconceived α=0.05. Mean Time: (ẍ) 16 Standard Deviation (Ơ) .8 Sample Size (n): 15 Significance Level (x): .05 Null Hypothesis u=16.43 Alternative Hypothesis u < 16.43 Rule: Reject Null Hypothesis if X > P-Value Minitab Calculations: One-Sample Z Test of μ = 16.43 vs < 16.43 The assumed standard deviation = 0.8 N Mean SE Mean 95% Upper Bound Z P 15 16.000 0.207 16.340 -2.08 0.019 P-Value is .019 Conclusion : Since X (.05) is > than the P-value (.019) the null hypothesis should be rejected. With this information, I am suggesting that Jeffery can in fact swim the 25-meter free-style faster than 16.43 seconds if he does have the new goggles.
Problem 2 A college football coach thought that his players could bench press an average of 275 pounds. It is known that the standard deviation is 55 pounds. Three of his players thought that the average was  more than  that amount. They asked  30  of their teammates for their estimated maximum lift on the bench press exercise. The data ranged from 205 pounds to 385 pounds. The actual different weights were (frequencies are in parentheses) 205(3); 215(3); 225(1);  241(2); 252(2); 265(2); 275(2); 313(2); 316(5); 338(2); 341(1); 345(2); 368(2); 385(1). Conduct a hypothesis test using a 2.5% level of significance to determine if the bench press average is more than 275 pounds . Mean Weight: (ẍ) 286.2 Standard Deviation (Ơ) 55 Sample Size (n): 30 Significance Level (x): .025 Null Hypothesis: µ = 275 Alternative Hypothesis: u > 275 Rule: Reject Null Hypothesis if P-Value < .025 Minitab Calculations: One-Sample Z Test of μ = 275 vs > 275 The assumed standard deviation = 55 N Mean SE Mean 97.5% Lower Bound Z P 30 286.2 10.0 266.5 1.12 0.132 P-value is .132
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