This t-distribution is actually an entire family of distributioncurves, not unli

Question

This t-distribution is actually an entire family of distributioncurves, not unlike the normal distributions. Whereas a normaldistribution is identified by its mean and standard deviation, at-distribution is characterized by an integer number called itsdegrees of freedom (abbreviated d.f.). These t-distributionsare mound-shaped and centered at zero, but they are more spread out(i.e., they have wider, fatter/taller tails) than a normaldistribution. As the number of degrees of freedom increases,the tails get narrower and the t-distribution gets closer andcloser to a normal distribution. That a peek at Chapter 18 tohelp with this last part. Use the fact that df = n-1. Table Cgives critical values (t*) for various degrees of freedom.
l) What is the value of t* you should use for a 98%confidence interval?

m) If the sample standard deviation is $867.35,re-calculate the confidence interval using the correct standarddeviation and critical value.

n) How do the two intervals compare(size-wise)? Which one is more realistic? Why?

Explanation / Answer

l) What is the value of t* you should use for a 98% confidenceinterval? df = 82-1 = 81 ==> 2.373 m) If the sample standard deviation is $867.35,re-calculate the confidence interval using the correct standarddeviation and critical value. ME = 2.373*867.35/(82) = 227 ==> 857±227 = (630,1084) n) How do the two intervals compare(size-wise)? Which one is more realistic? Why? THE T-INTERVAL IS WIDER. IT IS MORE REALISTIC BECAUSE IT IS BASEDON THE ACTUAL DATA, RATHER THAN A GUESS ABOUT THE STANDARDDEVIATION.

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