To monitor the acid mine pollution from Philsaga Mining Corporation, two independent sampling stations were chosen. One located downstream from the acid mine discharge point and the other located upstream. For 12 monthly samples collected at the downstream station the species diversity index had a mean value of 3.11 and a standard deviation of 0.771, while 10 monthly samples collected at the upstream station had a mean index value 2.04 and a standard deviation of 0.448.
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- Unfortunately, arsenic occurs naturally in some ground water. A mean arsenic level of m= 8.0 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 37 tests gave a sample mean of xbar= 7.2 ppb arsenic, with s= 1.9 ppb. Does this info indicate that the mean level of arsenic in this well is less than 8ppb? Use a= 0.01. Show full detail.A regulation lacrosse ball should weigh 154 grams. A company produces lacrosse balls for the PLL. To help ensure a high degree of accuracy, a random sample of 20 lacrosse balls is drawn from the production line every 45 minutes and each lacrosse ball is measured for accuracy. If the average weight of the sample is found to be significantly different than 154 grams, then the production line is shut down for inspection. The mean weight of a recent sample of 20 lacrosse balls was found to be 167.98 grams. Use the p-value method to test the hypothesis that the mean weight of a lacrosse ball produced by this company is different than 154 grams, using α=0.02α=0.02. Assume that the distribution of weights of all lacrosse balls produced by this company is known to be approximately normally distributed with a standard deviation of 21.6 grams. State the null and alternative hypothesis for this test. H0= H1= Determine the test statistic for the hypothesis test. Round the solution to two decimal…The intelligence quotients (IQs) of 16 students from one area of a city showed a mean of 107 and a standard deviation of 10, while the IQs of 14 students from another area of the city showed a mean of 112 and a standard deviation of 8. Use alpha = 0.01. What is the pooled standard deviation?
- The coating thickness of plastic film in millimeters (mm) on a substrate material is tested using two difference temperatures which are 125°F and 150°F. The substrate material with temperature of 125°F is normally distributed with a mean coating thickness of 103.5mm and a standard deviation of 10.2mm. While the substrate material with temperature of 150°F also are normally distributed with a mean coating thickness of 99.7mm and a standard deviation of 16.imm. Random samples of 11 substrates are coated at 125°F and 13 substrates are coated at 150°F. a) Construct the sampling distribution of the difference in means of coating thickness between two temperatures. b) Find the probability that the mean coating thickness for temperature of 125°F exceed 110mm.Unfortunately, arsenic occurs naturally in some ground water. A mean arsenic level of mu equals 8.0 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 36 test gave a sample mean of x-bar = 6.9 ppb arsenic, with s = 2.6 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Alpha = 0.01. a) What is the level of significance? b) What is the value of the sample test statistic? Round answer to 3 decimal places. c) estimate the p-value?A commercial on Station A has a mean length of 35 seconds with a standard deviation of 8 seconds. Station B has a mean commercial length of 30 seconds with a standard deviation of 5 seconds. Compare the relative dispersion of the two stations.
- A soft-drink machine is regulated so that the amount of drink dispensed averages 240 milliliters with a standard deviation of 15 milliliters. Periodically, the machine is checked by taking a sample of 40 drinks and computing the average content. If the mean of the 40 drinks is a value within 2 standard deviations from the mean , the machine is thought to be operating satisfactorily; otherwise, adjustments are made. If the company official found the mean of 40 drinks to be 236 milliliters and concluded that the machine needed no adjustment. Was this a reasonable decision?Avalanches can be a real problem for travelers in the western United States and Canada. Slab avalanches studied in Canada had an average thickness of µ = 67 cm. A sample of 31 avalanches in the U.S. gave a sample mean of = 63.0 cm. It is known that o = 10.3 cm for this type of data. Use a 0.03 level of significance to test the claim that the mean slab thickness of avalanches in the United States is different from that in Canada. Use the P-Value Approach. What is the Decision for this problem? O There is not sufficient evidence at the 0.03 level of significance to show that the mean slab thickness of avalanches in the United States is different from that in Canada. There is sufficient evidence at the 0.03 level of significance to show that the mean slab thickness of avalanches in the United States is less than that in Canada. There is sufficient evidence at the 0.03 level of significance to show that the mean slab thickness of avalanches in the United States is different from that in…