The output from a statistical software package indicates that the mean and stand

Question

The output from a statistical software package indicates that the mean and standard deviation of a data set consisting of 100 measurements are exist1, 500 and exist300, respectively. a. What are the units of measurement of the variable of interest? A. Units B. Dollars C. Single measurements Based on the units, what type of data is this, quantitative or qualitative? The data is b. What can be said about the number of measurements between exist900 and exist2, 100? That of the measurements are between exist900 and exist2, 100. What can be said about the number of measurements between exist600 and exist2, 400? That of the measurements are between exist600 and exist2, 400. What can be said about the number of measurements between exist1, 200 and exist1, 800? That of the measurements are between exist1, 200 and exist1, 800. What can be said about the number of measurements between exist1, 500 and 2, 100? That of the measurements are between exist1, 500 and 2, 100.

Explanation / Answer

SOLUTION: IN the example the sample mean= 1500 and standard deviation =300.

a) Well in this example there is only one unit we can see that is " DOLLARS"
based on that this data is "QUANTITATIVE" .

b)Since here no information is given about the shape of the data set we can only use the Chebyshev's rule:
i)The measurement are between $900 and $2100 have 2 stadared deviations below the mean and 2 stadared deviation above the mean using chebys
1500 - 2 (300) = 900
1500 + 2 (300) = 2,100
So, The probability that | Sample mean - true mean| > 2 SD
=> 1-(1/2)^2 = 3/4 = 0.75
About 75 % of the data fall between $900 and $2,100 .

ii) The measurement are between $600 and $2400 is:
here the measurement are between $600 and $2400 have 3 stadared deviations below the mean and 3 stadared deviation above the mean using chebyshev's tule:
The probability that | Sample mean - true mean| > 3 SD
1500-3(300) = 600
1500+3(300) = 2,400
=>1- (1/3)^2 = 1-1/9 = 8/9 =0.8888
About 89 % of values fall between 600 and 2,400 .

iii) The measurement are between $1200 and $1800 is:
$1200 have 1 standard deviation below and 1 standard deviation above the mean so if we use the chebyshv's rule nothing can be said about the number of measurement that will fall between $1200 and $1800.

iv) Here 1500 is equal to the mean and 2100 is 2 standard devaions above the so using chebyshv's rule at least 75% of the measurements will fall between 900 and 2100 it is possible that all of the 75% measurements will be bwtween 900 and 1500 thus nothing can be said about the number of measurements between 1500 and 2100

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