"You toss a coin 163 times and get 50 heads. Test the hypothesis that it is a fair coin, using a two-tailed test and 5% level of significance. The answer wants each of the following: test statistic, critical value, and accept or reject the hypothesis. It is quite obvious to me that we will reject the null hypothesis since the 2 z-scores associated with getting less than 50 tails (50.5 using continuity correction) are -4.86 and 4.86, while at a 5% confidence interval, the two z-scores are -1.96 and 1.96, but I am not sure what he wants for the test statistic or critical value, or what those are exactly."

overrated3245w 2022-09-30 Answered
You toss a coin 163 times and get 50 heads. Test the hypothesis that it is a fair coin, using a two-tailed test and 5% level of significance.
The answer wants each of the following: test statistic, critical value, and accept or reject the hypothesis.
It is quite obvious to me that we will reject the null hypothesis since the 2 z-scores associated with getting less than 50 tails (50.5 using continuity correction) are -4.86 and 4.86, while at a 5% confidence interval, the two z-scores are -1.96 and 1.96, but I am not sure what he wants for the test statistic or critical value, or what those are exactly.
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Answers (2)

Jase Powell
Answered 2022-10-01 Author has 11 answers
Since 50 heads out of 163 is a proportion, we should use the relevant one-sample z-test (we can do so since 163 is a large number):
z = ( p ^ p 0 ) n p 0 ( 1 p 0 )
Here
H 0 : p = p 0 = 1 2 H 1 : p 1 2
p ^ = 50 163 = 0.307 n = 163
so the test statistic is
z = ( 0.307 0.5 ) 163 0.5 × 0.5 = 4.928
The critical values are ± 1.960 as you thought. Since 4.928 falls outside [ 1.960 , 1.960 ], we reject the null hypothesis and conclude the coin is biased.
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dannyboi2006tk
Answered 2022-10-02 Author has 2 answers

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