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We want to test the hypothesis that a sou is well balanced, that is to say...

We want to test the hypothesis that a sou is well balanced, that is to say that the probability of having face is the same as that of having pile. We take α = 0.10.

a) If, in fact, the probability of facing is 0.54 and if it is thrown under 1000 times, what is the probability that the null hypothesis will be rejected?

b) If the probability of having face is 0.54, how many times does the penny have to be launched so that the probability that the null hypothesis will be rejected is 95%?

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

a)

The null and alternative hypotheses are defined as,

This is a two tailed test.

The z-statistic is,

The p-value for the z statistic is obtained using the z distribution table,

The probability that the null hypothesis will be rejected = 1-0.0114=0.9886

b)

The probability that the null hypothesis will be rejected = 0.95.

The z score for the p-value is obtained from the standard normal distribution table (for two tailed test)

The z-statistic is,

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