The response time of a computer system to a request for a ce

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

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	0.595564

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

The response time of a computer system to a request for a ce

Solution

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