Question

5) A book claims that more hockey players are born in January through March than in October through December. The following data show the number of players selected in a draft of new players for a hockey league according to their birth month. Is there evidence to suggest that hockey players' birthdates are not uniformly distributed throughout the year? Use the level of significance

alpha equalsα=0.05

Birth Month	Observed Count	Expected Count
January-March	60
April-June	51
July-September	26
October-December	37

4) A traffic safety company publishes reports about motorcycle fatalities and helmet use. In the first accompanying data table, the distribution shows the proportion of fatalities by location of injury for motorcycle accidents. The second data table shows the location of injury and fatalities for

2084

riders not wearing a helmet. Complete parts (a) and (b) below.

Location of injury	Observed Count	Expected Count
Multiple Locations	1049
Head	866
Neck	3535
Thorax	89
Abdomen/Lumbar/Spine	45

1)

Determine the expected count for each outcome.		n=605
		i	1	2	3	4
		pi	0.16	0.44	0.24	0.16

What is the expected count for outcome 1 is ( ) ?

3) The first significant digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8, or 9. It was discovered that first digits do not occur with equal frequency. Probabilities of occurrence to the first digit in a number are shown in the accompanying table. The probability distribution is now known as Benford's Law. For example, the following distribution represents the first digits in

206

allegedly fraudulent checks written to a bogus company by an employee attempting to embezzle funds from his employer. Complete parts (a) through (c) below.

Distribution of first digits (Benford's Law)
Digit	1	2	3	4	5
Probability	0.301	0.176	0.125	0.097	0.079
Digit	6	7	8	9
Probability	0.067	0.058	0.051	0.046

First digits in allegedly fraudulent checks
First digit	1	2	3	4	5	6	7	8	9
Frequency	36	25	28	20	23	36	15	16	7

Answer 1

(3)

$$ \begin{array}{l} \chi^{2}=\sum\left(\frac{\left(O_{i}-E_{i}\right)^{2}}{E_{i}}\right) \\ \text { whre, } E_{i}=N * \text { Probability } \mathrm{N}=238 \end{array} $$

\(\therefore \chi^{2}=58.380\)