Question

The time (in minutes) between requests for the hookup of electric service was accurately recorded at...

The time (in minutes) between requests for the hookup of electric service was accurately recorded at the Gowatts Flash and Flicker Company, with the results for the last 50 requests given in column A. Test the following hypotheses using the Chi-squared goodness of fit test and using a significance level (α) of 5%. Calculate the p-value for both problems and state the conclusions (reject or fail to reject Ho.

1. Ho: time between requests come from an Exponential distribution with mean 5 minutes

Follow what we discussed in class; that is, use equal-probability intervals and use as many intervals as possible such than n/k >= 5.

Note that the intervals are designed so that the expected number of observations in each interval is the same.

2. Ho: time between requests come from an Exponential distribution with the mean equal to the sample mean

Follow what we discussed in class; that is, use equal-probability intervals and use as many intervals as possible such than n/k >= 5.

Note that the intervals are designed so that the expected number of observations in each interval is the same.

(Hint: fill the cells in the table with the correct numbers or formulas and draw a conclusion about the hypothesis.

You can use the array function =Frequency() to get the Oi's, or use a functions like

COUNTIF($A$2:$A$51,"<="&E4) - COUNTIF($A$2:$A$51,"<="&D4) if you know how to use them OR sort the observations from smallest to largest and count them by hand.

For the value of the Chi2Dist you look it up in the Chi2 table )

Obs
0.661
5.124
13.509
15.512
2.731
2.42
6.255
6.892
12.413
4.37
4.91
15.033
5.745
2.758
6.892
2.984
27.969
13.243
2.169
0.377
8.989
58.091
0.651
17.602
16.713
10.613
12.107
12.711
0.921
9.063
12.801
1.543
0.965
6.675
5.692
3.827
4.636
3.411
1.9
1.875
20.249
3.624
62.146
11.209
6.636
10.244
7.093
7.897
0.315
0.79

Homework Answers

Answer #1

1.

Upper class boundary Probability Expected frequency (=E) Observed Frequency(=O)
0-1.1157 0.2 10 7 0.9
1.1157-2.5541 0.2 10 5 2.5
2.5541-4.5815 0.2 10 7 0.9
4.5815-8.0472 0.2 10 12 0.4
8.0472 and more 0.2 10 19 8.1
12.8

2.

Upper class boundary Probability Expected frequency (=E) Observed Frequency(=O)
0-2.1107 0.2 10 10 0
2.1107-4.8320 0.2 10 10 0
4.8320-8.6673 0.2 10 11 0.1
8.6673-15.2239 0.2 10 12 0.4
15.2239 and more 0.2 10 7 0.9
Total 1.4

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