An amateur golfer wishes to determine if there is a difference between the drive distances of her two favorite drivers. (A driver is a specialized club for driving the golf ball down range.) She hits fourteen balls with driver A and 10 balls with driver B. The drive distances (in yards) for the trials are show below. Driver A 282 246 253 302 264 248 275 214 269 283 303 257 233 279 Driver B 249 235 251 269 218 252 220 292 263 239 Assume that the populations are approximately normal. Construct a 90% confidence interval for the difference between the mean drive distances for the two drivers. Based on your results, is it reasonable to conclude that the mean drive distances may be the same for drivers A and B? A) Yes B) No
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For Driver A: Mean (µ_A) = (282 + 246 + 302 + 264 + 248 + 275 + 214 + 269 + 283 + 303 + 257 + 233 + 279) / 14 ≈ 265.93 Standard Deviation (σ_A) = √[(Σ(x - µ_A)^2) / (n_A - 1)] ≈ 25.34 For Driver B: Mean (µ_B) = (249 + 235 + 291 + 269 + 218 + 252 + 220 + 292 + Show more…
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An amateur golfer wishes to determine if there is a difference between the drive distances of her two favorite drivers. (A driver is a specialized club for driving the golf ball downrange.) She hits fourteen balls with driver A and ten balls with driver B. The drive distances (in yards) for the trials are shown below. Driver A: 265, 278, 299, 314, 243, 248, 275, 276, 265, 266, 277, 248, 276, 282 Driver B: 233, 220, 217, 239, 235, 245, 261, 194, 272, 233 Assume that the populations are approximately normal. Can you conclude that there is a difference in the mean drive distances for the two drivers? Use the α = 0.05 level of significance. Use the 6-step p-value method.
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An amateur golfer wishes to determine if there is a difference between the drive distances of her two favorite drivers. (A driver is a specialized club for driving the golf ball down range.) She hits fourteen balls with driver A and 10 balls with driver B. The drive distances (in yards) for the trials are summarized below. For driver A, the sample mean and sample variance are 262.3 and 370.8, respectively. For driver B, the sample mean and sample variance are 234.9 and 488.8, respectively. Assume that the populations are approximately normal with unknown variances. What is the p-value for testing whether the average drive distance by driver A is longer than that by driver B? Use the α = 0.05 level of significance. 0.005 < p-value < 0.01 0.01 < p-value < 0.02 0.025 < p-value < 0.05 0.05 < p-value < 0.10 A random sample of 80 adults is chosen and their mean serum cholesterol level is found to be 202 milligrams per deciliter. Assume that the population standard deviation is 40. Based on a 95% confidence interval for the mean serum cholesterol, is it likely that the mean serum cholesterol is greater than 219? (Hint: you should first construct the 95% confidence interval.) Yes The likelihood cannot be determined. No
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Driving distance 2011 How far do professional golfers drive a ball? (For non-golfers, the drive is the shot hit from a tee at the start of a hole and is typically the longest shot.) The next page shows a histogram of the average driving distances of the 186 leading professional golfers by end of November 2011 along with summary statistics (www.pgatour.com). Graph cannot copy a) Find a 95% confidence interval for the mean drive distance. b) Interpreting this interval raises some problems. Discuss. c) The data are the mean driving distance for each golfer. Is that a concern in interpreting the interval? (Hint: Review the What Can Go Wrong warnings of Chapter 8. Chapter 8?! Yes, Chapter 8.)
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