The following data give the recovery of bromide from spiked samples of vegetable matter, measured using a gas-–liquid chromatographic method. The same amount of bromide was added to each specimen. 764 ug g 782 ug g Tomato: 777 790 773 759 790 770 758 Cucumber: 782 778 765 789 797 (a) Test whether the recoveries from the two vegetables have variances which differ significantly. (b) Test whether the mean recovery rates differ significantly.
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- Much concern has been expressed regarding the practice of using nitrates as meat preservatives. In one study involving possible effects of these chemicals, bacteria cultures were grown in a medium containing nitrates. The rate of uptake of radio-labeled amino acid (in dpm, disintegrations per minute) was then determined for each culture, yielding the following observations. 7,255 6,875 9,637 6,863 9,098 5,846 8,954 7,979 7,068 7,498 7,882 8,179 7,528 8,728 7,469 Suppose that it is known that the mean rate of uptake for cultures without nitrates is 8,000. Do the data suggest that the addition of nitrates results in a decrease in the mean rate of uptake? Test the appropriate hypotheses using a significance level of 0.10. Find the test statistic and P-value. (Use technology to calculate the P-value. Round your test statistic to two decimal places and your P-value to three decimal places.) t= P-value= State your conclusion. Reject H0. We have convincing evidence that the mean rate of…Calculate the average values of the Cp and Cpk capabil-ity indices for the BOD data , assuming that LSL=5 mg/L and USL=35 mg/L. Do these val-ues of the indices indicate that the process performance is satisfactory?Suppose that samples of polythene bags from two manufacturers A and B are tested by a prospective buyer for bursting pressure, with the following results: If the prices are the same, which manufacture’s bags would be preferred by the buyer? Why?
- Consider the following 10 measurements about the cohesion of a soil: 12 kPa, 14 kPa, 15 kPa, 14.5 kPa, 16.0 kPa, 18 kPa, 15 kPa, 16.2 kPa, 17. 6 kPa, 13 kPa. Work out the solutions of the following two problems, assuming the cohesion follows the normal and lognormal distributions, respectively. (1) Draw the PDF of the cohesion; (2) Evaluate the probability that the cohesion based on the PDF is less than 5 kPa, 10 kPa, and 15 kPa; (3) Assess the effect of the type of distribution on the results.Below are pupil sizes from two samples: 8 men and 8 women (measured in millimeters). Test the hypothesis that thee is a difference in pupil sizes between males and females, using an alpha level of .01. Males Females 7.7 8.9 7.5 8.7 6.9 9.0 7.8 8.8 7.7 7.9 6.9 8.8 4.5 9.0 7.5 9.0 What is the Critical Value?In experiments to determine the effectiveness of drugs such as anti-fungal ointments that are applied to the skin, the concentration of the drug in a patient’s skin must be measured. The article “Determining Bioequivalence of Topical Dermatological Drug Products by Tape- Stripping” (W. Navidi, A. Hutchinson, et al., Journal of Pharmacokinetics and Pharmacodynamics, 2008:213–220) describes an improved method of measuring that is designed to ensure that all the drug in the skin is recovered. Assume that in an experiment using the old method, the mean amount of drug recovered from a sample of 49 patients was 105 ng with a standard deviation of 20 ng, and that in an experiment using the new method the mean amount of drug recovered in a sample of 35 patients was 117 ng with a standard deviation of 15 ng. Find a 98% confidence interval for the difference in the mean amounts recovered between the two methods.
- What is the critical value? Wj\hat is the p value?Find the mean and variance of the gamma distributionusing integration to obtain E(X) and E(X2).[Hint: Express the integrand in terms of a gammadensity.]In a clinical trial of ciprofloxacin (CIPRO), pediatric patients were initiated on 6 to 10 mg/kg intravenously every 8 hours and converted to oral therapy, 10 to 20 mg/kg, every 12 hours Calculate the ranges of the total daily amounts of ciprofloxacin that would have been administered intrave nously and orally to a 40-lb child
- The diameter of a metal shaft used in a disk-drive unit is normally distributed with mean 0.2508 in. and std. dev. 0.0005 in. The specification on the shaft have been established as (0.25-0.0015 in, 0.25+0.0015in) If the process mean has been adjusted to 0.25 in, what fraction of the shafts produced does NOT conform to specifications? a). 0.0027 b). 0.0013 c).0.08 d). 0.16In a survey of 180 females who recently completed high school, 75% were enrolled in college. In a survey of 160 males who recently completed high school, 70% were enrolled in college. At α=0.07, can you reject the claim that there is no difference in the proportion of college enrollees between the two groups? Assume the random samples are independent. Complete parts (a) through (e). Find the critical value(s) and identify the rejection region(s).The Board of Transportation and Safety (BTS) wants to examine the safety mechanisms of A, B, and C-class cars. Samples of 10 cars for each class were used. The board members collect the pressure exerted overall on the driver’s body during an impact test. Assume alpha of 0.05. What is dfbetween = ? What is dfwithin = ? What is the critical test statistic: ? A B C 27 21 48 13 23 39 11 10 22 15 27 30 34 34 31 n(A) = 5 n(B) = 5 n(B) = 5 T(A)=100 T(B)=115 T(C)=170 SS(A)=86 SS(B)=135 SS(C)=151 What is the MSbetween=? What is the MSwithin=? What is the calculated test statistic? Given the values of your critical test statistic and calculated test statistic, do you reject the null?