Choosing Lottery Numbers: In the Super-Megalottery there are 50 numbers (1 to 50), a player chooses tendifferent numbers and hopes that these get drawn. If the player'snumbers get drawn, he/she wins an obscene amount of money. Thetable below displays the frequency with which classes of numbersare chosen (not drawn). These numbers came from a sample of 180chosen numbers.
Chosen Numbers (n = 180)
| 1 to 10 | 11 to 20 | 21 to 30 | 31 to 40 | 41 to 50 |
| Count | 42 | 54 | 27 | 34 | 23 |
|
The Test: Test the claim that all chosen numbersare not evenly distributed across the five classes. Test this claimat the 0.01 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 asother entries for that column.
| Chosen | Observed | Assumed | Expected | |
| i | Numbers | Frequency(Oi) | Probability(pi) | FrequencyEi | |
| 1 | 1 to 10 | 1 | 0.2 | 36.0 | 1.000 |
| 2 | 11 to 20 | 54 | 2 | 36.0 | 9.000 |
| 3 | 21 to 30 | 27 | 0.2 | 3 | 2.250 |
| 4 | 31 to 40 | 34 | 0.2 | 36.0 | 4 |
| 5 | 41 to 50 | 23 | 0.2 | 36.0 | 4.694 |
| | | |
| ? | | n = 180 | | | ?2 = 5 |
|
(b) What is the value for the degrees of freedom? 6
(c) What is the critical value of
?2
? Use the answer found in the
?2
-table or round to 3 decimal places.
t? = 7
(d) What is the conclusion regarding the null hypothesis?
reject H0 fail to rejectH0
(e) Choose the appropriate concluding statement.
We have proven that all chosen numbers are evenly distributedacross the five classes. The data supports the claim that allchosen numbers are not evenly distributed across the five classes. There is not enough data to support theclaim that all chosen numbers are not evenly distributed across thefive classes.
