SOLUTION: A die is tossed 180 times with the following results: Is this a halanced die? Use a 0.01 level of significance. 10.80 In 100 tosses of a coin, 63 heads and 37 tails are ohserve

Algebra ->  Probability-and-statistics -> SOLUTION: A die is tossed 180 times with the following results: Is this a halanced die? Use a 0.01 level of significance. 10.80 In 100 tosses of a coin, 63 heads and 37 tails are ohserve      Log On


   

Question 980421: A die is tossed 180 times with the following
results:
Is this a halanced die? Use a 0.01 level of significance.
10.80 In 100 tosses of a coin, 63 heads and 37 tails
are ohserved. Is this a balanced coin? Use a 0.05 level
of significance.
Kindly, Any one can advice my about it ?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Looks like you have an incomplete first problem and a complete second problem.
Here's what to do for both but I'll only use data from the second.
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Hypothesis testing with a proportion.
Balanced die would mean p%5Bh%5D=0.5.
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Null hypothesis : p%5Bh%5D=0.5
Alternate hypothesis : p%5Bh%5D%3C%3E0.5
Two tailed test, assume normality since N%3E30
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Find the standard deviation.
sigma=sqrt%28%28p%281-p%29%29%2FN%29
sigma=sqrt%28%280.63%280.37%29%29%2F100%29
sigma=0.04828
Find the z score.
z=%28p%5Bh%5D-p%29%2Fsigma
z=%280.5-0.63%29%2F0.04828
z=-2.6926
For 0.05 significance, the critical z score would be,
z%5Bc%5D=-1.96
Since you are outside the "fail to reject" region, you reject the null hypothesis.
It is not a fair die.