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Questions 1:
Use the following values from a student’s t-distribution to establish a 95% confidence interval for the population mean given a sample size of 10, a sample mean of 6.25, and a sample standard deviation of 12. Assume that the population from which the sample is drawn is normally distributed and that the population variance is not known.
The 95% confidence interval is closest to a:
A、 lower bound of –2.20 and an upper bound of 14.70.
B、 lower bound of –0.71 and an upper bound of 13.21.
C、 lower bound of –2.33 and an upper bound of 14.83.
Questions 2:
Which of the following statements is most accurate? The first quintile generally exceeds the:
A、 first quartile.
B、 median.
C 、first decile.
View answer resolution
【analysis】
C is correct. With a sample size of 10, there are 9 degrees of freedom. The confidence
interval concept is based on a two-tailed approach. For a 95% confidence interval, 2.5%
of the distribution will be in each tail. Thus, the correct t-statistic to use is 2.262. The
confidence interval is calculated as:
【analysis】
C is correct. The first quintile is the 20th percentile (a percentile indicates the value below
which a given percentage of observations in a group fall). The first decile is the 10th
percentile, the first quartile is the 25th percentile, and the median is the 50th percentile.
Although it is possible that these various percentiles or some subsets of them might be
equal (for example, the 10th percentile possibly could be equal to the 20th percentile),
in general, the order from smallest to largest would be: first decile, first quintile, first
quartile, median.
B is incorrect. The first quintile is the 20th percentile. The first decile is the 10th percentile, the first quartile is the 25th percentile, and the median is the 50th percentile.
A is incorrect. The first quintile is the 20th percentile. The first decile is the 10th percentile, the first quartile is the 25th percentile, and the median is the 50th percentile.
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