Question

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

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