Calculate a 95% prediction interval for the predicted stopping distance at 15mph

Question

Calculate a 95% prediction interval for the predicted stopping distance at 15mph?

Last week we looked at data studying the (predictable) relationship between speed and stopping distance, and we found that stopping distances could be approximated with the least squares equation listed below. Also listed are some predictive standard errors needed to solve the following problems. y = -17.8ft + 3.946 ft/mph times x n = 50 when x = 15 mph SE_mu = 2.181 SE_y = 15.53 when x = 24 mph SE_mu = 4.183 SE_y = 15.94 1.a) Calculate a 95% prediction interval for the predicted stopping distance at 15 mph.

Explanation / Answer

Ans:

When x=15

y=-17.8+3.946*15=41.39

n=50

df=50-2=48

t* for 95% Confidence and df=48 is 2.011

95% confidence interval: 37.00481 45.77519

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