4. The summary statistics for the scores on the first semester final for a large statistics class are shown in
the table below. To investigate if the sample maximum was an unbiased estimator of the population
maximum, the professor of the class selected 100 SRSS of size n = 10 for all of the students' scores on the
exam. The sample maximum for each of these samples was recorded on the dotplot below. The mean of
the simulated sampling distribution of the maximums, 430.5, is indicted by the vertical line segment.
Does the sample maximum appear to be an unbiased estimator of the population maximum?
N
mean
Min
SD
61.40 128
137
349.11
dh
Q₁
309
med
354
Q₁
393
Max
472
350
sample maximam
a. Yes, because the sampling distribution of the maximum is approximately normal.
b. No, because the mean of the simulated sampling distribution, 430.5, is not approximately 349.11,
c. Yes, because 7 of the 100 samples had maximums of approximately 472.
d. No, because the mean of the simulated sampling distribution is 430.5, which is not approximately 472.