text: # Approximate Confidence Interval Estimates of U Stats Assignment Homework Help
  
  Approximate Confidence Interval Estimates of U
  
  In the usual situation encountered in practice, we do not know the value of  and we are not sure the population is normally distributed. However, we do know (Chapter 9) that for samples of more than 30 (n > 30), the distribution of sample means is nearly normal even though the population is not normal. Second, experimentation has shown t distributions for n > 30 provide good approximations of confidence intervals for skewed (non normal)populations which are uni modal (have one peak). Third, as we saw in Table 10.2, t distributions are nearly normal when n is more than 30. Statisticians have used the foregoing three facts to formulate a rule of thumb, which is as follows: When az is not known, but n > 30, estimate az by sz, but use the.
  
  of sulfur oxides is between 7.2 and 11.8 tons per day.
  In the example, if we had known U’z, and it was 3.24 tons per day, we
  would have used ZO.025 = 1.96 rather than t = 2.26 in construction of the interval.
  The result would have been the more precise (narrower) interval
  
  In general, interval estimates of J.L are more precise when we know U’z than.
  when we do not know U’z and have to estimate it from a sample.
  EXERCISE See the last example. Suppose that for another random sample,
  this time with n = 16 days, the sample mean emission is 10.3 tons per day and
  the sample standard deviation is 3 tons per day. Construct a 90 percent confidence
  interval estimate of u:
  ANSWER 9.0 ~ p: ~ 11.6 tons per day.
  
  Posted on August 27, 2014 in STATISTICAL INFERENCE ESTIMATION
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