A random sample of size n was taken from a population and a 90 % confidence interval was
computed. For the purposes of this problem, we will assume that the observed interval is
( 2.3 , 3.4 ). Indicate whether each of the following statements is True or False.
______A. The interval ( 2.3 , 3.4 ) may or may not contain µ . However, in the long run,
about 90 out of every 100 intervals computed in the same manner will contain µ .
______B. There is a 90 % probability that µ will lie in the interval ( 2.3 , 3.4 ) .
______C. The probability that a future value of the sample mean will lie in the interval
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( 2.3 , 3.4 ) is 0.90 .
______D. If we were to apply the procedure that produced (2.3 , 3.4) repeatedly to different
samples, approximately 90 % of the intervals would contain µ .
______E. The interval ( 2.3 , 3.4 ) may or may not contain µ . However, if ten such
intervals are computed from ten different samples, exactly 9 of the 10 would
contain µ , and one would not.
______F. In the long run, the chances are 90 % that µ will fall within the interval
( 2.3 , 3.4 ) .
______G. Exactly 90 % of the original population lies within the interval ( 2.3 , 3.4 ) .
______H. The sample mean is always in our confidence interval for µ .
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______I. It is not always the case that µ is in the confidence interval.
______J. When the sample size is increased, one expects the width of the confidence
interval to decrease.
