Question

• Specify hypothesis, define the parameter and population of interest

• Identify the test-statistic and its sampling distribution

• Fins the test-statistic value and its associated P-Value

• Use your P-Value state your statistical conslusion

• Interpret your conclusion in the context of the proble

Doing deucedly difficult duty, daring distaff detective Sheerluck Hopeless draws dire data-driven deductions, discouraging dastardly dangerous deeds during deep, dark Decembers. Disturbingly daft Dr. Witless, Sheerluck’s stumpling sidekick, shares Sheerluck’s adventures with the public. Agile agent and annoyingly anal analyst Sheerluck Hopeless tracks her diabolical nemesis, the pompously pedantic Professor Marionasty, and his cowardly Lieutenant Colonel D. Jean Moutarde.

1. Blightly blarney but blissfully blase bloodhound Sheerluck Hopeless has trained herself to recognize at a glance suspect heights and weights. From experience she has found that her estimation errors tend to follow approximately normal distributions. Hopeless tests her estimation abilities on five London constables: her estimate erros, in cm and kg, are given in the table below:

	Hopeless Errors
Heights (cm)	-0.6	-0.2	0.2	0.5	0.6
Weights (kg	-1.2	-0.7	-0.1	0.1	0.9

1. Find a 95% confidence interval for the mean difference between Sheerluck’s errors in estimating suspect heights and weights.

2. Test that there IS a difference between Sheerluck’s mean estimation errors for suspect heights and weights against the hypothesis of NO difference.

• For parts a. and b. should treat Sheerluck’s data as if they were the SAME measurments on two samples of 5 DIFFERENT constables

3. Compare Sheerluck’s estimation errors for heights against weights:

I. Draw a simple plots of weight errors (y) against errors (x).

II. Find the correlation coefficient between Sheerluck’s two types of error.

III. Find the regression line for weight errors as a function of height errors.

IV. Use the coefficient of variation to interpret how well this linear model explains the relationship between Sheerluck’s height and weight estimation errors.

• For part c. should treat Sheerluck’s data as if they were two DIFFERENT measurments on the SAME set of constables

Answer 1

ANSWER

b)

i)

ii)

r = 0.9563

iii)

y^ = -0.353 + 1.53 x

iv)

R^2 = 0.9144

it means 91.44 % of variaiton in weight is explained by height