(2 points) an article in the washington post on march 16, 1993 stated that nearly 45 percent of all americans have brown eyes. a random sample of n=76n=76 americans found 28 with brown eyes. we test h0: p=.45 ha: p≠.45

(a) what is the z-statistic for this test?

(b) what is the p-value of the test?

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

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