3. Suppose you want to test (statistically) whether or not a given coin is biase

Question

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

Explanation / Answer

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.

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