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Quesation 1:
For the single line the mean is 7.13 minutes and the median is 7.1
minutes. For the individual lines the mean the mean is also 7.13 and the
median is also 7.1 minutes. We can say the means and medians for the two
sets are equal without doing a formal hypothesis test. The main difference
in the two sets is the variability. The standard deviation of the single line set
is .476 and for the individual lines set it is 1.786. So, the individual line set
has more variability.
Question 2:
The range is the ddifference between the largest and smallest values.
In this case 0.91 – 0.64 = 0.27 mm. The varince = .009147 and standard
deviation = .0956. If the fruit flies from the city sampled were
representative of all fruit flies in the country then the standard deviation
would serve as a reasonable estimate of all fruit flies in the country.
Otherwise, the standard deviation from the sample would not serve as
reasonable estimate.
Question 3:
146 to 188 is the mean plus and minus 3 SDs. The emperical rule
says that about 99.7% of all values of a normal distribution lie bwtween plus
and minus 3 SDs. 153 to 181 is the mean plus and minus 2 SDs. The
emperical rule says that about 95% of all values of a normal distribution lie
bwtween plus and minus 2 SDs.
Question 4:
Converting the temps to a standard normal variate we get
Z = (Mean – u) / SD = (-1.66 - 0) / 1 = -1.66 and for mean of
1.66 we get 1.66. Using the standard normal table or calculator we find that
P(-1.66 < z < 1.66) = 1 - .097 = .903.
Question 5:
As above, using the standard normal table or calculator we find that
P(-1.43 < z < 1.43) = 1 - .1528 = .8472.
Question 6:
Before 1983: mean = 3.1134, median = 3.1065
After 1983: mean = 2.4926, median = 2.4931
The before 1983 weights are less than the after 1983 weights. This
difference is statistically significant (p<.0001).
Question 7:
Range = 3 (4-1), variance = .6642, and SD = .8127. Although a
decrease of 4 is at the extreme of the observed sample values it probably is
not unusual.
Question 8:
Range = 237 (444 – 207), variance = 3134.12, SD = 55.98. The SD
decreases to 30.22 when the largest value of 444 is deleted – a 54%
decrease.
Question 9:
The range rule of thumb says SD = range / 4. From this you get
range = 4*SD = 4*490 = 1960. So the range of consumption amounts would
be from 2222 to 4182 (4182 – 2222 = 1960 and centered on the mean =
3202). The range limits, 2222 and 4182, are the minimum and maximum
“usual” amounts. The value of 2202 lies outside these two values so it
might be considered unusual.
Question 10:
Chebyshev’s theorem says at least (1 – 1 / k*k) of the data will lie
within k SDs of the mean. So, we know that at least 89% of womens heights
are within 3 SDs of the mean. Mean plus and minus 3 SDs is 159 plus and
minus 21. So the minimum height would be 138 and the maximum would
be 180.
Question 11:
This question is not clear. It is “Find the indicated critical value.
Z^.05=_” If it means the 0.05 level of significance Z value it is 1.96.
Question 12:
Mean = 54.1, median = 51, midrange = (35 + 83) / 2 = 59. Since
each value occurs only once in this sample there is no mode.
Estimate of total number of defined words is 1495*54.1 = 80,880.
Since the sample was a random sample, the estimate of the total number of
words is likely an accurate estimate.