The accompanying data table lists the magnitudes of 50 earthquakes measured on the Richter scale. Test the claim that the population of earthquakes has a mean magnitude greater than 1.00. Use a 0.01 significance level. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, and conclusion for the test. Assume this is a simple random sample.
0.710
0.740
0.640
0.390
0.700
2.200
1.980
0.640
1.220
0.200
1.640
1.320
2.950
0.900
1.760
1.010
1.260
0.000
0.650
1.460
1.620
1.830
0.990
1.560
0.390
1.280
0.830
1.330
0.540
1.250
0.920
1.000
0.790
0.790
1.440
1.000
2.240
2.500
1.790
1.250
1.490
0.840
1.420
1.000
1.250
1.420
1.350
0.930
0.400
1.390
=>
Identify the test statistic.
(round to two decimal places)
Identify the P-value.
(round to three decimal places as needed)
Fail to reject H0. There is insufficient evidence?
|
Leading Digit
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
|---|---|---|---|---|---|---|---|---|---|
|
Benford’s Law
|
30.1%
|
17.6%
|
12.5%
|
9.7%
|
7.9%
|
6.7%
|
5.8%
|
5.1%
|
4.6%
|
|
Leading Digits of Inter-Arrival Traffic Times
|
76
|
62
|
29
|
33
|
19
|
27
|
28
|
21
|
22
|
|
Test Statistic, X^2:
|
20.9222
|
|---|---|
|
Critical X^2:
|
15.5073
|
|
P-Value:
|
0.0074
|
Because the leading digits of inter-arrival traffic times ▼ (fit or do not fit) the distribution described by Benford’s law, it appears that those times ▼ (are not or are) typical. There is ▼ (a good chance or very little chance) that the computer has been hacked. Corrective action ▼ (is not or is) needed.
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