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11. (A: 6 marks) (a) Conduct a hypothesis test to determine whether getting 52 tails in 100 coin tosses is sufficient to show that the coin is unbiased (b) Construct a 93% confidence interval for the proportion of tossing tails if getting 52 tails in 100 coin tosses, rounding the calculation results to 4 decimals in this question. Totally 100 marks]
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0.5 unbiased a) Alternative hypothesis;H1: Null hypothesis;Ho 0.5 biased Sample proportion: P.52 Here,x- 52 Sample size nF100 given Standard error: 0.05 say 0.05 given Level of significance Critical values: Test statistic: a t 1.96 p- p P(1-P 0.40 p(l-p p-value For Za 0.400 the two tailed p-value is 0.6892 Decision: Since p-value > α, do not reject H0 Conclusion: There is sufficient evidence to show that coin is unbiased

b)Sample number of even Sample size: Sample proportion Level of significancee Two tailed critical value: 52 given n= 100 given 2X p---0.520 0.07 given 93% level 1.812 from z table Margin of error: = 0.0905 1 Lower limit: 0.4295 P+E= 0.6105 Upper limit: The confidence interval is 0.4295 Sps 0.6105

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