I am not sure how to correctly distinguish and form conclusions between the two
ID: 3204019 • Letter: I
Question
I am not sure how to correctly distinguish and form conclusions between the two histograms. Please explain to me how to do so and answer the questions
The following three histograms (A, B, and C) plot information about the number of hours of sleep adult Europeans get per night (Roenneberg 2012). One of them shows the frequency distri- bution of individual values in a random sample. Another shows the distribution of sample means for samples of size 10 taken from the same population. Another shows the of sample means for samples of size 100.Explanation / Answer
a) B shows the frequency distribution of individual values as these are samples of size 1 and so histogram is widest. A is much narrower than B and represents the frequency distribution of sample means of size 10 and finally C having the thinnest frequency distribution is that for sample means of size 100.
b) Let us assume that the sleep any person gets is independent of all other persons and for every individual the exact amount of sleep for each person belongs to the same distribution as all others. The as sample sizes go up the sample means will more closely approximate the true population mean and the variability among the means will go down. So with increasing sample size we expect the histograms will become thinner and closely packed.
c) By eye approximation from B we conclude that mean number of hours of sleep is between 8 to 9 hours.
d) By eye approximation from C we conclude that mean of the frquency distribution of sample means is between 7.5 to 8 hours
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