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Answer: a) z=1.43
b) 0.1528
Step-by-step explanation:
The given set of hypothesis :
Since the alternative hypothesis is two-tailed , so we perform two-tailed test.
Also, it is given that : A random sample of n=76 Americans found 28 with brown eyes.
Sample proportion:
a) The z-statistic would be :-
b) P-value for two-tailed test = 2P(Z>|z|)= 2P(z>|-1.43|)
=2P(z>1.43)
=2(1-P(z≤1.43)
=2-2P(z≤1.43)
= 2-2(0.9236)[Using standard z-table]
= 2-1.8472=0.1528
Hence, the P-value of the test= 0.1528