Question

Sample means 2.7 2.9 3.4 3.7 4.2 4.3 4.3 4.4 4.5 4.5 4.6 4.6 4.7 4.7 4.7 4.7 4.8 4.8 5 5 5 5.1 5.1 5.2 5.2 5.3 5.4 5.4 5.5 5.5 5.9 6 6.1 6.1 6.1 6.2 6.2 6.3 6.3 6.4 6.4 6.6 6.7 6.9 6.9 7 7 7.1 7.2 7.5 7.8 8.1 8.3

(d) (3 pts) The average number of letters per word in the population of all 268 words is μ-4295. Mark this value on the histogram in (b). How many students produced a sample average greater than the actual population average? (Count the number of students form the actual data file). What proportion of the students is this? (e) (3pts) What is the average of the sample means in the class? Is this value larger or smaller than the population mean u 4.295 letters? When the sampling method produces characteristics of the sample that systematically differ from those characteristics of the population, we say that the sampling method is biased. () (3 pts) Would you say that this sampling method (asking people to simply circle ten representative words) is biased? If so, in which direction, towards smaller words or larger words? Explain how you can tell this from the histogram. (g) (3 pts) Consider a different sampling method: close your eyes and point to the page ten times iin order to select the words for your sample. Would this sampling method also be biased? Explain

Answer 1

a.

Class sample mean) 2--3 3--4 4--5 5--6 6--7 7--8 8--9 Total Frequency 17 1 53

b.

2-3 3-4 4-5 5--6 6-7 7--8 8--9 Class

c. Frequency of class interval of sample mean.

d.

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No. of students produced a sample average greater than the actual population average=53-5=48

e. sample mean=5.55283; it is larger than population mean.