3 Suppose you want to test statistically whether or not a gi

3. Suppose you want to test (statistically) whether or not a given coin is biased . So you toss the coin 30 (independent) times, then observe the number of heads X that turns up and set the following decision rule:

Accept if Ho: p=1/2 if 5<x<25

Reject Ho:p=1/2

and accept the alternative hypothesis if Ha: p= 1/2X 5 or X 25

. (3 pts) Calculate / tabulate for p = .1, .2, .3, .4, .5, .6, .7, .8, .9 b. (5 pts) Graph versus p using Excel. Discuss your graph. c. (5 pts) Get a quarter and toss it 30 times and record the number of heads. On the basis of this outcome, state whether you will accept or reject according to the decision rule set out above.

x	P1	P2	P3	P4	P5	P6	P7	P8	P9
0	0.04239	0.00124	0.00002	0	0	0	0	0	0
1	0.1837	0.01052	0.00031	0	0	0	0	0	0
2	0.41135	0.04418	0.00211	0.00005	0	0	0	0	0
3	0.64744	0.12271	0.00932	0.00031	0	0	0	0	0
4	0.82451	0.25523	0.03015	0.00151	0.00003	0	0	0	0
5	0.92681	0.42751	0.07659	0.00566	0.00016	0	0	0	0
6	0.97417	0.60697	0.15952	0.01718	0.00072	0.00001	0	0	0
7	0.99222	0.76079	0.28138	0.04352	0.00261	0.00005	0	0	0
8	0.99798	0.87135	0.43152	0.09401	0.00806	0.00022	0	0	0
9	0.99955	0.93891	0.58881	0.17629	0.02139	0.00086	0.00001	0	0
10	0.99991	0.97438	0.73037	0.29147	0.04937	0.00285	0.00004	0	0
11	0.99998	0.99051	0.84068	0.43109	0.10024	0.0083	0.00016	0	0
12	1	0.99689	0.91553	0.57847	0.1808	0.02124	0.00063	0	0
13	1	0.9991	0.95995	0.7145	0.29233	0.04811	0.00212	0.00001	0
14	1	0.99977	0.98306	0.82463	0.42777	0.09706	0.00637	0.00005	0
15	1	0.99995	0.99363	0.90294	0.57223	0.17537	0.01694	0.00023	0
16	1	0.99999	0.99788	0.95189	0.70767	0.2855	0.04005	0.0009	0
17	1	1	0.99937	0.97876	0.8192	0.42153	0.08447	0.00311	0
18	1	1	0.99984	0.9917	0.89976	0.56891	0.15932	0.00949	0.00002
19	1	1	0.99996	0.99715	0.95063	0.70853	0.26963	0.02562	0.00009
20	1	1	0.99999	0.99914	0.97861	0.82371	0.41119	0.06109	0.00045
21	1	1	1	0.99978	0.99194	0.90599	0.56848	0.12865	0.00202
22	1	1	1	0.99995	0.99739	0.95648	0.71862	0.23921	0.00778
23	1	1	1	0.99999	0.99928	0.98282	0.84048	0.39303	0.02583
24	1	1	1	1	0.99984	0.99434	0.92341	0.57249	0.07319
25	1	1	1	1	0.99997	0.99849	0.96985	0.74477	0.17549
26	1	1	1	1	1	0.99969	0.99068	0.87729	0.35256
27	1	1	1	1	1	0.99995	0.99789	0.95582	0.58865
28	1	1	1	1	1	1	0.99969	0.98948	0.8163
29	1	1	1	1	1	1	0.99998	0.99876	0.95761
30	1	1	1	1	1	1	1	1	1

Sample size = 30 ( I.e use Z test)

H0 p = 1/2 5 < x < 25

Probability of head = 1/2

Probability of tails = 1/2

If p = 1/2 then it\'s not baised else it\'s baised.

Mu = n p = 30 x 1/2 = 15

S.d = Root npq = root 30 x 1/2 x1/2 = 2.738

Z = (5 - 15) / 5.476 < Z(x) < (25 - 15 ) / (2.738 / root 30) = 10 / 5.476

=0.9663 - .0336 = 0.9327

Accept H0

That\'s means the coin is not baised.

3. Suppose you want to test (statistically) whether or not a given coin is biased . So you toss the coin 30 (independent) times, then observe the number of head

3 Suppose you want to test statistically whether or not a gi

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