I really need help with this question, a quick reply would be very much apprecia
ID: 3221207 • Letter: I
Question
I really need help with this question, a quick reply would be very much appreciated
http://www.chegg.com/homework-help/bias-roulette-bettingthe-game-roulette-consists-wheel-38-col-chapter-12-problem-5c-solution-9781305480483-exc
I did post the question it's in the link but I guess I'll type it out?
The game of roulette consists of a wheel with 38 coloured and numbered slots. The numbers are 1 to 36. Half of the slots are red and the other half are black. The wheel is spun and an iron ball is rolled, which eventually comes to rest in one of the slots. Gamblers can make several different kinds of bets. Most players bet on one or more numbers or on a colour (black or red). Here is the layout of the roulette table:
3R 6 9R 12R 15 18R 21R 24 27R 30R 33 36R
2 5R 8 11 14R 17 20 23R 26 29 32R 35
1R 4 7R 10 13 16R 19R 22 25R 28 31 34R
(R meaning red)
Two statisticians recorded bets on 904 spins. There were 21,731 bets. Researchers want to examine middle bias which is the tendency for guessed in multiple choice situations to select middle answers. For example, if there are five choices A, b, c, d, and e, guessed will tend to choose c.
Most players stand on both sides of the table so that the middle numbers are 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, and 35.
A. If there is no middle bias, what proportion of the bets will be on 1 of the 12 middle numbers?
B. Conduct a test at the 5%significance level to determine whether middle bias exists.
C. The middle on the middle are the numbers 17 and 20. If there is no middle bias, what proportion of the bets will be either 17 or 30?
D. Test with a 5% significance level to determine whether middle bias exists.
Explanation / Answer
A)If there is no middle bias, then all the 38 numbers have equal proportion of bets . So, proportion of bets for any one of the 12 middle numbers will be 1:38
B)Here is the test to determine whether middle bias exists:
The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis:Middle bias exist P = 1/12= 0.083
Alternative hypothesis:Middle bias does not exist P 1/12
If there will be no middle bias then proportion of bets for one of the middle no will be p= 1/38=0.026
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample proportion is too big or if it is too small.
For this analysis, the significance level is 0.05. Sample bets = 21731
Using sample data, we calculate the standard deviation () and compute the z-score test statistic (z).
= sqrt[ P * ( 1 - P ) / n ] = sqrt [(0.083 * 0.97) / 21731] = 0.001
z = (p - P) / = (.026-.083)/0.001 = 30.411
The p value is 0. Since the P-value (0.0) is smaller than the significance level (0.05), we reject the null hypothesis.
C) If there was no middle bias, then the proportion of bes either for 17 or 20 will 2:38
D)
Here is the test to determine whether middle of middle bias exists:
The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis:Middle bias exist P = 2/12= 0.083
Alternative hypothesis:Middle bias does not exist P 2/12
If there will be no middle bias then proportion of bets for one of the middle no will be p= 2/38=0.052
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample proportion is too big or if it is too small.
For this analysis, the significance level is 0.05. Sample bets = 21731
Using sample data, we calculate the standard deviation () and compute the z-score test statistic (z).
= sqrt[ P * ( 1 - P ) / n ] = sqrt [(0.166 * 0.833) / 21731] = 0.002
z = (p - P) / = (.05-0.16)/0.002 = 45.107
The p value is 0. Since the P-value (0.0) is smaller than the significance level (0.05), we reject the null hypothesis.