Using a graphical display, determine whether the data appear to be a random sample

financial statement claims an inventory that averages 300 per item. An auditor’s random sample of 20 items yielded a mean and standard deviation of 160 and 90, respectively. Do the data con- tradict the hospital’s claimed mean value per inventoried item and indicate that the average is less than 300? Use a ⫽ .05. Bus. 5.68 Over the past 5 years, the mean time for a warehouse to fill a buyer’s order has been 25 min- utes. Officials of the company believe that the length of time has increased recently, either due to a change in the workforce or due to a change in customer purchasing policies. The processing time in minutes was recorded for a random sample of 15 orders processed over the past month. 28 25

27 31

10 26

30 15 55 12

24 32

28 42 38 Do the data present sufficient evidence to indicate that the mean time to fill an order has increased? Engin. 5.69 If a new process for mining copper is to be put into full-time operation, it must produce an average of more than 50 tons of ore per day. A 15-day trial period gave the results shown in the accompanying table. Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Yield tons 57.8 58.3 50.3 38.5 47.9 157.0 38.6 140.2 39.3 138.7 49.2 139.7 48.3 59.2 49.7

a. Estimate the typical amount of ore produced by the mine using both a point estimate

and a 95 confidence interval.

b. Is there significant evidence that on a typical day the mine produces more than

50 tons of ore? Test by using a ⫽ .05. Env. 5.70 The board of health of a particular state was called to investigate claims that raw pollu- tants were being released into the river flowing past a small residential community. By applying financial pressure, the state was able to get the violating company to make major concessions to- ward the installation of a new water purification system. In the interim, different production sys- tems were to be initiated to help reduce the pollution level of water entering the stream. To monitor the effect of the interim system, a random sample of 50 water specimens was taken throughout the month at a location downstream from the plant. If ⫽ 5.0 and s ⫽ .70, use the sample data to determine whether the mean dissolved oxygen count of the water in ppm is less than 5.2, the average reading at this location over the past year. a. List the five parts of the statistical test, using a ⫽ .05. b. Conduct the statistical test and state your conclusion. Env. 5.71 The search for alternatives to oil as a major source of fuel and energy will inevitably bring about many environmental challenges. These challenges will require solutions to problems in such areas as strip mining and many others. Let us focus on one. If coal is considered as a major source of fuel and energy, we will have to consider ways to keep large amounts of sulfur dioxide SO 2 and particulates from getting into the air. This is especially important at large government and industrial operations. Here are some possibilities.

1. Build the smokestack extremely high. 2. Remove the SO

2 and particulates from the coal prior to combustion.

3. Remove the SO

2 from the gases after the coal is burned but before the gases are released into the atmosphere. This is accomplished by using a scrubber. A new type of scrubber has been recently constructed and is set for testing at a power plant. Over a 15-day period, samples are obtained three times daily from gases emitted from the stack. The amounts of SO 2 emissions in pounds per million BTU are given here: Day Time 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 6 A . M . .158 .129 .176 .082 .099 .151 .084 .155 .163 .077 .116 .132 .087 .134 .179 2 P . M . .066 .135 .096 .174 .179 .149 .164 .122 .063 .111 .059 .118 .134 .066 .104 10 P . M . .128 .172 .106 .165 .163 .200 .228 .129 .101 .068 .100 .119 .125 .182 .138 y