Al-Idrisi, who is visiting Stockholm for the first time, thinks that half of all

Question

Al-Idrisi, who is visiting Stockholm for the first time, thinks that half of all people in Sweden are blue-eyed. His friend Prof. Ingemar Rejectson wants to shows Al-Idrisi that the proportion is not so high, and suggests that they count the number of blue-eyed people passing by as they sit in a cafe?, sipping macchiato. They count 36 blue-eyed people among 99 passing by. Al- Idrisi, who studied economics at Koc?, quickly calculates the P-value and realizes that there is strong statistical evidence against his original assumption. Explain Al-Idrisi’s reasoning.

Explanation / Answer

Answer

Under the assumption of Al-Idrisi, that half of all people in Sweden are blue-eyed, (i.e., under the null hypothesis), the proportion of the blue-eyed among all people in Sweden must be ½ and hence the number of the blue-eyed in a sample of size n has Binomial Distribution, B(n, ½). And hence, given ‘They count 36 blue-eyed people among 99 passing by’, the p-value is the probability of 36 of B(99, ½), which by Excel Function, BINOMDIST(Number_s:Trials:Probability_s:Cumulative), is 0.001996 which is very small as viewed against the standard levels of significance of 5% and 1%. This implies that the chances of p being ½ is remote. Or in other words. The null hypothesis is not tenable.   

i.e., there is strong statistical evidence against his original assumption. ANSWER

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