The response time of a computer system to a request for a certain type of inform
ID: 3390453 • Letter: T
Question
The response time of a computer system to a request for a certain type of information is hypothesized to have an exponential distribution with parameter lamda=1 sec (so if X= response time, the pdf of X under Ho is f0(x)=e^(–x) for x>= 0.
a. If you had observed X1,X2,...,Xn and wanted to use the chi-squared test with five class intervals having equal probability under H0, what would be the resulting class intervals?
b. Carry out the chi-squared test using the follow- ing data resulting from a random sample of 40 response times: .10 .99 1.14 .79 1.16 1.76 .71 2.21 .68 .91 .55 .81 1.26 3.24 .12 .26 .80 .41 .59 .27 2.22 .66 .43 .11 .46 .69 .38 2.51 2.77 .16 1.1 1 .02 2.13 .19 1.21 1.13 2.93 2.14 .34 .44
Explanation / Answer
Sol)
Chisqaure
Chisqaure value= sum of ((Oi-Ei)2 /Ei)
=92.577
Oi Ei (oi-Ei) (Oi-Ei)^2 (Oi-Ei)^2 /Ei 10.99 1.33 9.66 93.3156 70.16211 1.14 1.33 -0.19 0.0361 0.027143 0.79 1.33 -0.54 0.2916 0.219248 1.16 1.33 -0.17 0.0289 0.021729 1.76 1.33 0.43 0.1849 0.139023 0.71 1.33 -0.62 0.3844 0.289023 2.21 1.33 0.88 0.7744 0.582256 0.68 1.33 -0.65 0.4225 0.317669 0.91 1.33 -0.42 0.1764 0.132632 0.55 1.33 -0.78 0.6084 0.457444 0.81 1.33 -0.52 0.2704 0.203308 1.26 1.33 -0.07 0.0049 0.003684 3.24 1.33 1.91 3.6481 2.742932 0.12 1.33 -1.21 1.4641 1.100827 0.26 1.33 -1.07 1.1449 0.860827 0.8 1.33 -0.53 0.2809 0.211203 0.41 1.33 -0.92 0.8464 0.636391 0.59 1.33 -0.74 0.5476 0.411729 0.27 1.33 -1.06 1.1236 0.844812 2.22 1.33 0.89 0.7921 0.595564 0.66 1.33 -0.67 0.4489 0.337519 0.43 1.33 -0.9 0.81 0.609023 0.11 1.33 -1.22 1.4884 1.119098 0.46 1.33 -0.87 0.7569 0.569098 0.69 1.33 -0.64 0.4096 0.30797 0.38 1.33 -0.95 0.9025 0.678571 2.51 1.33 1.18 1.3924 1.046917 2.77 1.33 1.44 2.0736 1.559098 0.16 1.33 -1.17 1.3689 1.029248 1.1 1.33 -0.23 0.0529 0.039774 1.02 1.33 -0.31 0.0961 0.072256 2.13 1.33 0.8 0.64 0.481203 0.19 1.33 -1.14 1.2996 0.977143 1.21 1.33 -0.12 0.0144 0.010827 1.13 1.33 -0.2 0.04 0.030075 2.93 1.33 1.6 2.56 1.924812 2.14 1.33 0.81 0.6561 0.493308 0.34 1.33 -0.99 0.9801 0.736917 0.44 1.33 -0.89 0.7921 0.595564Related Questions
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