Choosing Lottery Numbers: In the Super-Mega lottery there are 50 numbers (1 to 5

Question

Choosing Lottery Numbers: In the Super-Mega lottery there are 50 numbers (1 to 50), a player chooses ten different numbers and hopes that these get drawn. If the player's numbers get drawn, he/she wins an obscene amount of money. The table below displays the frequency with which classes of numbers are chosen (not drawn). These numbers came from a sample of 180 chosen numbers.

Chosen Numbers (n = 180)

The Test: Test the claim that all chosen numbers are not evenly distributed across the five classes. Test this claim at the 0.05 significance level.

(a) The table below is used to calculate the test statistic. Complete the missing cells.
Round your answers to the same number of decimal places as other entries for that column.

(b) What is the value for the degrees of freedom?  

(c) What is the critical value of

2

? Use the answer found in the

2

-table or round to 3 decimal places.
t =  

(d) What is the conclusion regarding the null hypothesis?

reject H0

fail to reject H0    

(e) Choose the appropriate concluding statement.

We have proven that all chosen numbers are evenly distributed across the five classes.

The data supports the claim that all chosen numbers are not evenly distributed across the five classes.

There is not enough data to support the claim that all chosen numbers are not evenly distributed across the five classes.

1 to 10 11 to 20 21 to 30 31 to 40 41 to 50 Count     43     41     31     33     32  

Explanation / Answer

a)

b)

degrees of freedom =categories-1=5-1=4

c)

critical value of 2 at 0.05 level =9.488

d) fail to reject H0 (as test statistic is less than critical value

e)There is not enough data to support the claim that all chosen numbers are not evenly distributed across the five classes.

i Numbers Frequency (Oi) Probability (pi) Frequency Ei (Oi Ei)2 Ei 1 1 to 10 43 0.2 36 1.361 2 11 to 20 41 0.2 36 0.694 3 21 to 30 31 0.2 36 0.694 4 31 to 40 33 0.2 36 0.250 5 41 to 50 32 0.2 36 0.444 n = 180 2 = 3.44

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