6. An environmental attorney is planning an investigation about the mean arsenic

Question

6. An environmental attorney is planning an investigation about the mean arsenic level in the blood of all residents, of all ages, who live in a certain community (about 20,000 people). a) Suppose she wants to estimate the mean level to within .02 mg/l with 98% confidence and the standard deviation is believed to be roughly .05 mg/l. How many observations should she obtain? For ethical, public health and other reasons, the attorney can get blood samples only from adults (age 18 years or older) who are willing and who are not hospitalized or under medical care for a life-threatening illness. Identify the target and sampled populations. Should the attorney be concerned about bias in her results? Why or why not? b) Fuller Bottle Company is designing a new plastic bottle which is supposed to be both cheaper and stronger than their current design. Impact strength was measured on a sample of 120 bottles. The results are shown in the histogram below. 7. a) Describe the basic features of the distribution. b) The sample mean and variance of the impact strength are 86.190 and 3.6334, respectively. Obtain a 98% confidence interval for the true mean strength. Is it plausible that the true mean is 87.0? Explain

Explanation / Answer

7)

Based on the distribution of the histogram , apparently the meausre of central tendency lies close to 87. Also , the shape of the distribution tells us that it is not close to normal . It also exhibits signs of bimodality as there is a peak 82-83 level

b) The mean = 86.190 and sd = 3.6334

so Ci is given as

mean +- z*SD/sqrt(n) , here n = 120 bottles and z = 2.33 for 98% CI from the z tables

86.190 +-2.33*3.6334/sqrt(120), solving this and getting the range

85.4171 and 86.96

so we are 98% confident that the true mean would lie in the range 85.41 and 86.96

as 87 does not fall within the 98% range , hence we are 98% sure that true mean is less than 86.96 and greater than 85.41. however , there is still a chance of 2% that the true mean is 87.

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