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If you are suspicious of the chance a candidate being chosen is 1/4, and a sample...

If you are suspicious of the chance a candidate being chosen is 1/4, and a sample of 6 random and independent people show the rate in which the candidate to be chosen to be 1/2 (where 3 approve and 3 disapprove). Given, with a α = 0.05, is this enough information to prove that chance in which the candidate to be chosen is higher than 1/4.

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Answer #1

Proportion (p0) = 1/4 =0.25

Total number of sample (n) = 6

number of favourable events (X) = 3

We are interested in testing the hypothesis

Since, the test is two-tail test at \alpha = 0.05

Decision Rule: Reject the null hypothesis if the test statistic value is greater than the critical value 1.64

The statistic value, 1.4142 is less than the critical values 1.64. Therefore, we fail to reject the null hypothesis.

We have insufficient information to prove that chance in which the candidate to be chosen is higher than 1/4.

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