A researcher constructed a 95 percent confidence interval for the mean number of alfalfa weevils on an alfalfa plant within a field. Based on 80 randomly selected alfalfa plants, the researcher found an average of 2.5 alfalfa weevils per plant and computed the 95 percent confidence interval to be 1.50 to 3.50. Which of the following statements is a correct interpretation of the 95 percent confidence level? (A) Approximately 95 percent of alfalfa fields sampled will have an average of 1.50 to 3.50 alfalfa weevils per plant, but nothing can be said about the sample mean number of alfalfa weevils for this or any other field. (B) Approximately 95 percent of alfalfa fields sampled will have an average of 1.50 to 3.50 alfalfa weevils per plant. The sample mean for this field was 2.50 alfalfa weevils per plant, but the sample means for other fields may be different. (C) If we repeatedly sampled this field, taking samples of 80 plants and constructing 95% confidence intervals, then, approximately 95 percent of these intervals would include 2.5, the mean for the sample described above. (D) If we repeatedly sampled this field, taking samples of 80 plants and constructing 95% confidence intervals, then, approximately 95 percent of these intervals would include the population mean number of alfalfa weevils on an alfalfa plant in this field. (E) If we repeatedly sampled this field, taking samples of 80 plants and constructing 95% confidence intervals, then, approximately 95 percent of these intervals would include the sample mean for that sample.
A researcher constructed a 95 percent confidence interval for the mean number of alfalfa weevils on an alfalfa plant
within a field. Based on 80 randomly selected alfalfa plants, the researcher found an average of 2.5 alfalfa weevils
per plant and computed the 95 percent confidence interval to be 1.50 to 3.50. Which of the following statements is a
correct interpretation of the 95 percent confidence level?
(A)
Approximately 95 percent of alfalfa fields sampled will have an average of 1.50 to 3.50 alfalfa weevils
per plant, but nothing can be said about the sample mean number of alfalfa weevils for this or any other
field.
(B)
Approximately 95 percent of alfalfa fields sampled will have an average of 1.50 to 3.50 alfalfa weevils
per plant. The sample mean for this field was 2.50 alfalfa weevils per plant, but the sample means for
other fields may be different.
(C)
If we repeatedly sampled this field, taking samples of 80 plants and constructing 95% confidence
intervals, then, approximately 95 percent of these intervals would include 2.5, the mean for the sample
described above.
(D)
If we repeatedly sampled this field, taking samples of 80 plants and constructing 95% confidence
intervals, then, approximately 95 percent of these intervals would include the population mean number
of alfalfa weevils on an alfalfa plant in this field.
(E)
If we repeatedly sampled this field, taking samples of 80 plants and constructing 95% confidence
intervals, then, approximately 95 percent of these intervals would include the sample mean for that
sample.
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