A coin is tossed 1000 times and 570 heads appear At alpha 00

A coin is tossed 1000 times and 570 heads appear. At alpha 0.05, test the claim that this is not a biased coin. Ho = Ha = Test Statistic = Alpha level of significance = Classical Critical Value = P-value = Conclusion =

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.5
Ha:   p   =/=   0.5 [ANSWER]
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As we see, the hypothesized po =   0.5      

Getting the point estimate of p, p^,          
          
p^ = x / n =    0.57      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.015811388      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    4.427188724   [ANSWER, TEST STATISTIC]

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significance level = alpha =   0.05   [ANSWER]

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As this is a two tailed 0.05 level test,

zcrit = +/- 1.96 [ANSWER]

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As this is a    2   tailed test, then, getting the p value,  
          
p =    9.54692*10^-6   [ANSWER]

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As P < 0.05, we REJECT THE NULL HYPOTHESIS.      

Thus, there is significant evidence that the coin is biased. [CONCLUSION]