Question

pose we are interested in finding the probability of a head in a coin, which may be loaded. The coin is tossed 100 times and 62 heads show up. If we are testing the null hypothesis that the coin is fair versus the alternate hypothesis that the coin is not fair, the value of the test statistic is given by 3 2.4 0.5 1.2

Answer 1

Solution :

Null and alternative hypotheses :

The null and alternative hypotheses would be as follows :

i.e. The coin is fair.

i.e. The coin is not fair.

Test statisic :

To test the hypothesis the most appropriate test is one sample z-test for proportion. The test statistic is given as follows :

Where, p̂ is sample proportion, p is hypothesized value of population proportion under H_{​​​​​​0}, q = 1 - p and n is sample size.

Sample proportion of heads is,

p = 0.50, q = 1 - 0.50 = 0.50 and n = 100

The value of the test statistic is 2.4.

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