The mean water temperature downstream from a discharge pipe at a power plant cooling tower should be no more than 100°F. The water temperature is measured on 10 randomly chosen days, and the results are shown below: 96.15 97.81 97.09 95.03 99.46 100.03 99.74 98.85 95.08 98.71 a. State the null hypothesis and alternative hypothesis for the above problem. b. Is there evidence that the water temperature is acceptable at 1% level of significance? c. Find the 95% confidence interval for the mean water temperature.
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- A quality inspector measured the diameter of a ball bearing using a new type of caliper. The results were as follows (in mm): 0.265, 0.263, 0.266, 0.267, 0.267, 0.265, 0.267,0.267, 0.265, 0.268, 0.268, and 0.263. Use the Wilcoxon signed-rank test to evaluate the claim that the mean ball diameter is 0.265 mm. Use a = 0.05. Match the answers. - v Parameter of Interest: a. H:u = 0.265 v Null and Alternative Hypothesis H:µ > 0.265 v Test Statistic: b. w = min (w+,w-) v Reject the Null Hypothesis if: c. Fail to reject the null hypothesis. v Conclusion: w = 9 is not less than or equal to the critical value w 0.05.1=9= 5 d. Mean ball diameter e. Reject the null hypothesis. The mean ball diameter claim is not 0.265 mm. f. H:u = 0.265 H:µ + 0.265 g.r = min (R+,R-) h. Η: μ:0.265 H:u < 0.265 i. w < wo.05. J=12 = 13 j. w < W0.05. n=9Watch your cholesterol: A sample of 290 patients between the ages of 38 and 82 were given a combination of drugs ezetimibe and simvastatin. They achieved a mean reduction in total cholesterol of 0.85 millimole per liter. Assume the population standard deviation is o =0.18.In a Q system, the demand rate for strawberry ice cream is normally distributed, with an average of 295 pints per week. The lead time is 6 weeks. The standard deviation of weekly demand is 16 pints. Refer to the standard normal table for z-values. a. The standard deviation of demand during the 6-week lead time is 39 pints. (Enter your response rounded to the nearest whole number.) b. The average demand during the 6-week lead time is 1770 pints. (Enter your response as an integer.) c. The reorder point that results in a cycle-service level of 96 percent is pints. (Enter your response rounded to the nearest whole number.)
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- Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 48 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that σ = 8.00 ml/kg for the distribution of blood plasma. When finding an 99% confidence interval, what is the critical value for confidence level? (Give your answer to two decimal places.) Z=0.005 (a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.) lower limit upper limit margin of error (b) What conditions are necessary for your calculations? (Select all that apply.) the distribution of volumes is normal ✔ is known o is unknown the distribution of volumes is…A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 182 lb and a standard deviation of 38 lb. The gondola has a stated capacity of 25 passengers, and the gondola is rated for a load limit of 3500 lb. Complete parts (a) through (d) below. a. Given that the gondola is rated for a load limit of 3500 Ib, what is the maximum mean weight of the passengers if the gondola is filled to the stated capacity of 25 passengers? The maximum mean weight is Ib. (Type an integer or a decimal. Do not round.) b. If the gondola is filled with 25 randomly selected skiers, what is the probability that their mean weight exceeds the value from part (a)? The probability is. (Round to four decimal places as needed.) c. If the weight assumptions were revised so that the new capacity became 20 passengers and the gondola is filled with 20 randomly selected skiers, what is the probability that their mean weight exceeds 175 lb, which is the…A given distribution has a population mean, μ, of 116 and a population standard deviation, σ, of 11. What z-score would be associated with the value x = 158?