Fumonisins are environmental toxins produced by a type of mold and have been found in corn and in products made from raw corn. The Center for Food Safety and Applied Nutrition provided recommendations on allowable fumonisin levels in human food and in animal feed based on a study of corn meal. The study compared corn meal made from partially degermed corn (corn that has had the germ, the part of the kernel located at the bottom center of the kernel that is used to produce corn oil, partially removed) and corn meal made from corn that has not been degermed. Specimens of corn meal were analyzed and the total fumonisin level (ppm) was determined for each specimen. Summary statistics for total fumonisin level from the U.S. Food and Drug Administration’s web site are given here.
- a. If the given means and standard deviations had been based on a random sample of 10 partially degermed specimens and a random sample of 10 specimens made from com that was not degermed, explain why it would not be appropriate to carry out a two-sample t test to determine if there is a significant difference in the
mean fumonisin level for the two types of corn meal. - b. Suppose instead that each of the random samples had included 50 com meal specimens. Explain why it would now be reasonable to carry out a two-sample t test.
- c. Assuming that each random
sample size was 50, carry out a test to determine if there is a significant difference in mean fumonisin level for the two types of com meal. Use a significance level of 0.01.
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Chapter 11 Solutions
Introduction To Statistics And Data Analysis
- Benzene is a pollutant that, according to studies, can be associated with health problems. Benzene is found in air, water, and soil and comes from both industrial and natural sources. Benzene levels in indoor air are generally higher than outdoors. The main source of benzene in indoor air appears to be tobacco smoke, thus the combustion of tobacco is a major source of pollution. Benzene levels are measured in a random sample of 36 bars in a city, obtaining an average benzene level of 19.2 mg / m3, with a standard deviation of 2.1 mg / m3. Estimate the mean benzene level in bars in this city using a 95% confidence interval. (do your calculations to 4 decimal places) (need the process can be by hand ,Excel or R.) a)Other solution b)[18.48946, 19.91054] c)[19.0950, 19.3050] d)[18.5140, 19.8859] e)[18.6243, 19.7757] f)[18.4315, 19.7936]arrow_forwardA 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_forwardDetermine the kurtosis if the data given is a sample.arrow_forward
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- Describe the "carry effect"arrow_forwardCash flow and profits are both crucial aspects of a business. Profit is the surplus revenue after deducting business expenses. Cash flow is the total amount of cash moving in and out of your business. For a business to be successful in the long term, it needs to generate profits while also operating with positive cash flow. During the Covid-19 pandemic, however, of a random sample of 199 auditors, 104 indicated some measure of agreement with this statement: cash flow is more important to keep the business operating on a day-to-day basis. a) Investigate the claim that one-half of the members of this population would agree with this statement. Also, find and interpret the p-value of this test. b) Find the probability of accepting the claim with a 10%-level test if, in fact, 60% of all auditors agree that cash flow is an important indicator to keep the business operating on a day-to-day basis.arrow_forwardWorkers in the office like to drink coffee during work. A doctor is concerned about this situation since the too much coffee consumption may result to long-term health problems. However, studies suggests that there is no risk in drinking three cups of coffee per day, which is about 250 mg of caffeine. The doctor wants to know if the amount of caffeine consumed by the workers is within tolerable limits. He randomly selected 20 students and found that they consume an average of 270 mg of caffeine each day with a standard deviation of 48 mg. Assume that the daily amount of caffeine consumed by students follow the normal distribution.1. Which of the following sets of hypotheses should be used in this study? A. Ho: μ = 250 vs. Ha: μ > 250 B. Ho: μ ≤ 250 vs. Ha: μ > 250 C. Ho: μ = 270 vs. Ha: μ > 270 D. Ho: μ = 270 vs. Ha: μ ≠ 270 2. Which of the following is(are) TRUE? I. The appropriate test procedure to answer the objective of the study is a…arrow_forward
- After stinging its victim, the honeybee leaves behind the barbed stinger, poison sac and muscles that continue to pump venom into the wound. Visscher et al. (1996) compared the effects of two methods of removing the stinger left behind: scraping off with a credit card or pinching off with thumb and index finger. A total of 40 stings were induced on volunteers. Twenty were removed with the credit card method and 20 were removed with the pinching method. The size of the subsequent welt by each measurement came from two volunteers (both authors of the study), each of whom received one treatment 10 times on the one arm and the other treatment 10 times on the other arm. Pinching led to a slightly smaller average welt, but the difference between the methods was not significant. Does this study include a control group? Enter the number of the best answer choice from the options below Yes, the control group is the group receiving the credit card method. Yes, the control group is the…arrow_forwardAnemia (low healthy blood cells or hemoglobin) has an important role in exercise performance. However, the direct link between rapid changes of hemoglobin and exercise performance is still unknown. A study investigated 18 patients with a blood disorder (beta-thalassemia). Participants in the study performed an exercise test before and the day after receiving a blood transfusion. Data are given in the table. HB = Hemoglobin RER = Respiratory exchange ID Change in HB Obese RER > 1.1 ratio No No 1 -1.4 No -1.5 No Yes No Yes 3 -2 No 4 -2.1 No -1.9 Yes Yes No -1.6 -1.8 -0.8 6 7 No Yes No Yes 8 9. -1 No No -1.2 No Yes 10 11 No No -0.8 -1.5 12 Yes No No Yes 13 14 -1.4 -2.6 -1.7 No No Yes Yes 15 Yes No Yes Yes 16 -2.6 No 17 18 -2.7 -1.5 Noarrow_forwardComposites are materials that are made by embedding a fiber, such as glass or carbon, inside a matrix, such as a metal or a ceramic. Composites are used in engineering structures, and their degradation when subjected to whether conditions is an important issue. In an experiment to investigate the effect of the moisture on a certain kind of composite, the weight gains of a collection of n=28 samples of composite subjected to water diffusion were obtained. The sample mean is x=0.42% with a sample std. of S=0.04% Can we 95% confident from the results of this experiment that the average weight gain for composites of this kind is smaller than 0.43%?arrow_forward
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