Your Practice Set – Applications and Interpretation for IBDP Mathematics
78
Paper 1 – Binomial and Poisson Variables
Example
A coin is tossed for 500 times . From the observation , 286 results are shown as ‘ Head ’ s .
A hypothesis test is conducted at a 5 % significance level to test whether the coin is biased such that the probability of getting a ‘ Head ’ is larger .
( a ) ( i ) Write down the null hypothesis of the test .
( ii ) Write down the alternative hypothesis of the test .
( b ) Find the p -value .
( c ) State the conclusion of the test with a reason .
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Solution
( a ) ( i ) H
0
: p � 0.5 A1
( ii ) H
1
: p � 0.5 A1
( b ) P ( X � 286 ) �1� P ( X � 285 )
( M1 ) for valid approach
P ( X �286 ) � 0.0007362287541 Thus , the p -value is 0.000736 .
( c ) |
The null hypothesis is rejected . |
A1 |
|
As p-value � 0.05
.
|
A1 |
A1
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