Here’s one to sink your teeth into: The authors of the article “Analysis of Food Crushing Sounds During Mastication: Total Sound Level Studies” (Journal of Texture Studies [1990]: 165–178) studied the nature of sounds generated during eating. Peak loudness (in decibels at 20 cm away) was measured for both open-mouth and closed-mouth chewing of potato chips and of tortilla chips. Forty subjects participated, with ten assigned at random to each combination of conditions (such as closed-mouth potato chip, and so on). We are not making this up! Summary values taken from plots given in the article appear in the accompanying table. For purposes of this exercise, suppose that it is reasonable to regard the peak loudness distributions as approximately normal.
- a. Construct a 95% confidence interval tor the (inference in mean peak loudness between open-mouth and closed-mouth chewing of potato chips. Interpret the resulting interval.
- b. For closed-mouth chewing (the recommended method!), is there sufficient evidence to indicate that there is a difference between potato chips and tortilla chips with respect to mean peak loudness? Test the relevant hypotheses using α = 0.01.
- c. The means and standard deviations given here were actually for stale chips. When ten measurements of peak loudness were recorded for closed-mouth chewing of fresh tortilla chips, the resulting mean and standard deviation were 56 and 14, respectively. Is there sufficient evidence to conclude that chewing fresh tortilla chips is louder than chewing stale chips? Use α = 0.05.
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Chapter 11 Solutions
Introduction to Statistics and Data Analysis
- In a study of exhaust emissions from school buses, the pollution intake by passengers was determined for a sample of nine school buses used in the Southern California Air Basin. The pollution intake is the amount of exhaust emissions, in grams per person, that would be inhaled while traveling on the bus during its usual 1818‑mile trip on congested freeways from South Central LA to a magnet school in West LA. (As a reference, the average intake of motor emissions of carbon monoxide in the LA area is estimated to be about 0.0000460.000046 grams per person.) The amounts for the nine buses when driven with the windows open are given. 1.151.15 0.330.33 0.400.40 0.330.33 1.351.35 0.380.38 0.250.25 0.400.40 0.350.35 A good way to judge the effect of outliers is to do your analysis twice, once with the outliers and a second time without them. Give two 90%90% confidence intervals, one with all the data and one with the outliers removed, for the mean pollution intake among all school buses…arrow_forwardQuestion #14 part A,B & C.arrow_forwardRothenberg et al. (A-13) investigated the effectiveness of using the Hologic Sahara Sonometer, a portable device that measures bone mineral density (BMD) in the ankle, in predicting a fracture. They used a Hologic estimated bone mineral density value of .57 as a cutoff. The results of the investigation yielded the following data: Confirmed Fracture BMD 1⁄4 :57ðTÞ BMD > :57ðT"Þ Total Present (D) 214 73 287 Not Present ðD" Þ Total 670 884 330 403 1000 1287 Source: Data provided courtesy of Ralph J. Rothenberg, M.D., Joan L. Boyd, Ph.D., and John P. Holcomb, Ph.D. (a) Calculate the sensitivity of using a BMD value of .57 as a cutoff value for predicting fracture and interpret your results. (b) Calculate the specificity of using a BMD value of .57 as a cutoff value for predicting fracture and interpret your results.arrow_forward
- A study was conducted to examine the effect of diet cola consumption on calcium levels in women. A sample of 16 healthy women aged 18 to 40 were randomly assigned to drink 24 ounces of either diet cola or water. Their urine was collected for three hours after ingestion of the beverage and calcium excretion (in mg) was measured. The data are stored in ColaCalcium.arrow_forwardThe paper "Accelerated Telomere Shortening in Response to Life Stress" (Proceedings of the National Academy of Sciences (2004): 17312-17315) described a study that examined whether stress accelerates aging at a cellular level. The accompanying data on a measure of perceived stress (x) and telomere length (y) were read from a scatterplot that appeared in the paper. Telomere length is a measure of cell longevity. 5.38 Perceived Telomere Perceived Telomere Stress Length Stress Length 5 1.25 20 1.22 1.32 20 1.30 1.5 20 1.32 7 1.35 21 1.24 10 1.3 21 1.26 11 1 21 1.30 12 1.18 22 1.18 13 1.1 22 1.22 14 1.08 22 1.24 14 1.3 23 1.18 15 0.92 24 1.12 15 1.22 24 1.50 15 1.24 25 0.94 17 1.12 26 0.84 17 1.32 27 1.02 17 1.4 27 1.12 18 1.12 28 1.22 18 1.46 29 1.30 19 0.84 33 0.94 a. Compute the equation of the least-squares line. b. What is the value of r? c. Does the linear relationship between perceived stress and telomere length account for a large or small proportion of the variability in telomere…arrow_forwardAn article contained the following observations on degree of polymerization for paper specimens for which viscosity times concentration fell in a certain middle range: 415 421 422 423 426 429 431 434 436 439 445 446 448 453 455 463 464 (a) Construct a boxplot of the data. O 420 420 430 430 440 440 450 The data appears to be centered near 438. The data is strongly skewed. There is one outlier. 450 Comment on any interesting features. (Select all that apply.) There are no outliers. The data appears to be centered near 428. There is little or no skew. 460 420 420 430 430 (b) Is it plausible that the given sample observations were selected from a normal distribution? Yes No 440 440 450 450 460 460 (c) Calculate a two-sided 95% confidence interval for true average degree of polymerization. (Round your answers to two decimal places.)arrow_forward
- PLS ANSWERarrow_forwardUse the information below to answer Questions #16 - 22. The article "Probabilistic Fatigue Evaluation of Riveted Railway Bridges" (J. of Bridge Engr., 2008: 237- 244) suggested the exponential distribution with A = 9 as a model for the distribution of stress range (MPa) in certain bridge connections. Find the mean. Round to four decimal places as needed.arrow_forwardAn article reported on a study in which each of 13 workers was provided with both a conventional shovel and a shovel whose blade was perforated with small holes. The authors of the cited article provided the following data on energy expenditure [kcal/kg(subject)/lb(clay)]. Worker: 2 4 5 6 Conventional: 0.0015 0.0015 0.0018 0.0022 0.001 0.0016 0.0028 Perforated: 0.0015 0.001 0.0019 0.0013 0.0011 0.0017 0.0024 Worker: 10 11 12 13 Conventional: 0.0021 0.0015 0.0014 0.0023 0.0017 0.002 Perforated: 0.0021 0.0013 0.0013 0.0017 0.0015 0.0013 n USE SALT Do these data provide convincing evidence that the mean energy expenditure using the conventional shovel exceeds that using the perforated shovel? Test the relevant hypotheses using a significance level of 0.05. (Use SALT to calculate the P-value. Use Hd = Hconventional - Hperforated Round your test statistic to one decimal place and your P-value to three decimal places.) t= df = p-value = State your conclusion. O we fail to reject H,. We have…arrow_forward
- In the article “The World's Longest Continued Series of Sea Level Observations” (M. Ekman, Paleogeography, 1988:73–77), the mean annual level of land uplift in Stockholm, Sweden, was estimated to be 4.93 ± 0.23 mm for the years 1774–1884 and to be 3.92 ± 0.19 mm for the years 1885–1984. Estimate the difference in the mean annual uplift between these two time periods, and find the uncertainty in the estimate.arrow_forwardA sample of 12 male and 12 female students were surveyed and the amount spent on food last week were recorded. The results are summarized in the table below. Test for the hypothesis that the weekly amount spent on food of male and female students is the same, at a=0.10. Male Female 623 685 537 629 613 517 588 580 651 658 688 582 526 614 579 528 814 655 878 804 660 549 722 617 a. What are the null and alternative hypotheses?b. What is the critical value? (4 decimal points)c. What is the test statistic? (4 decimal points)e. Reject or accept null hypothesis?arrow_forwardTo illustrate the effects of driving under the influence (DUI) of alcohol, a police officer brought a DUI simulator to a local high school. Student reaction time in an emergency was measured with unimpaired vision and also while wearing a pair of special goggles to simulate the effects of alcohol on vision. For a random sample of nine teenagers, the time (in seconds) required to bring the vehicle to a stop from a speed of 60 miles per hour was recorded. Complete parts (a) and (b). Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers. Click the icon to view the data table. (a) Whether the student had unimpaired vision or wore goggles first was randomly selected. Why is this a good idea in designing the experiment? O A. This is a good idea in designing the experiment because the sample size is not large enough. B. This is a good idea in designing the experiment because it controls for any "learning"…arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill