For each scenario described below, give a detailed complete description of the s

Question

For each scenario described below, give a detailed complete description of the steps required to compute the value using at TI84 calculator. No reference should be made to a Z table. If a particular statistical function is used, state its name and specify the entries you had to input to execute the function.

a) Assuming no raw data is given, you are told that a Normal Distribution applies, the mean of the normally distributed quantity is provided, and a particular percentile's value is specified; determine the standard deviation of the Normally distributed quantity

b) given the correlation, r, between two quantitative variables and the summary statistics for each of the two variables (which include the mean and std deviation for each variable), determine the equation of the regression line (for predicting the response variable from the explanatory variable)

c) compute the distance, measured in a number of std deviations, between a specific value of a quantitative variable and the mean of this variables distribution

Explanation / Answer

(a)

Assume the mean is given as X', the particular percentile is a% and the value at that percentile is X1.

Use the formula:

z = (X1-X')/SX

Normallly we would look into the z-table to find out what percentile value this 'z' corresponds to. But since percentile is given here, we simply put that value:

a/100 = (X1-X')/SX

From the above equation, solve for the unknown standard deviation SX by putting in all the other known values.

(b)

Given data:

Mean for x-values = X', SD for x-values = SX

Mean for y-values = Y', SD for y-values = SY

Correlation coefficient = r

Let the regression equation be:

Y = aX + b

Calculate a using:

a = r(SY/SX)

Then calculate b using:

b = Y' - aX'

(c)

Let the mean of the quatitative variable's measurement be X', and standard deviation be SX.

Let the specific value of the variable be X1.

So, the distance measured in number of standard deviations is: (X1-X')/SX

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