Answered: Histograms of random sample data are often used as an indication of the shape of the underlying population distribution. The histograms on below are based on…

MATLAB: An Introduction with Applications

6th Edition

ISBN: 9781119256830

Author: Amos Gilat

Publisher: John Wiley & Sons Inc

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Question

Histograms of random sample data are often used as an indication of the shape of the underlying population distribution. The histograms on below are based on random samples of size 30, 50, and 100 from the same population.

(a) Using the midpoint labels of the three histograms, what would you say about the estimated range of the population data from smallest to largest?

Complete the table giving the range of the sample data in each of the histograms.

	Smallest Value	Largest Value
Histogram (i)
Histogram (ii)
Histogram (iii)

Based on the completed table, select the most reasonable estimate of the range of the population data.

9.5 to 14

10 to 15

9 to 14

9 to 15

11 to 13

Does the bulk of the data seem to be between 10 and 14 in all three histograms?

Since there are no values outside the range 10 to 14, we can say that the bulk of the data is between 10 and 14.

Since there are very few values outside the range 10 to 14, we can say that the bulk of the data is between 10 and 14.

Since there are many values outside the range 10 to 14, we can say that the bulk of the data is not between 10 and 14.

Since there are very few outside the range 10 to 14, we can say that the bulk of the data is not between 10 and 14.

Since there are many values outside the range 10 to 14, we can say that the bulk of the data is between 10 and 14.

(b) The population distribution from which the samples were drawn is symmetric and mound-shaped, with the top of the mound at 12, 95% of the data between 10 and 14, and 99.7% of the data between 9 and 15. How well does each histogram reflect these characteristics? (Round your answers to one decimal place.)

The three histograms ______ (options: are, are not) mound-shaped and the data gradually reduces on either side of the mound in _______ (options: a symmetrical, and asymetrical) fashion. The highest bar in histogram (i) is at a value of x of _____ (fill in blank) units. The highest bar in histogram (ii) is at a value of x of ______ (fill in blank) units. The highest bar in histogram (iii) is at a value of x of ______ (fill in blank) units. So, the average top of the mound _______ (options: can, can not) be said to be at a value of x of approximately 12 units.

In histogram (i),______ % (fill in blank) of the sample data is between 10 and 14 inclusive, and _________% (fill in blank) of the sample data is between 9 and 15 inclusive. In histogram (ii),________% (fill in blank) of the sample data is between 10 and 14 inclusive, and _________% (fill in blank) of the sample data is between 9 and 15 inclusive. In histogram (iii), _______% (fill in blank) of the sample data is between 10 and 14 inclusive, and ________% (fill in blank) of the sample data is between 9 and 15 inclusive.

So, it ________ (is, is not) reasonable to say that 99.7% of population distribution data is between 9 and 15. Finally, the bulk of the sample data ___________(is, is not) between 10 and 14. So, it (is, is not) reasonable to say that 95% of the population distribution data is between 10 and 14.