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Hello students, let us do this question.
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Bit a, hypothesis to be tested here is for two population proportions equality.
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Null hypothesis is h0.
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Population proportion 1 is same as population proportion 2.
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Alternative hypothesis is population proportion 1 not equal to population proportion 2.
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Bit b, the z -test statistic for equality of two population proportions is z is equal to p1 minus p2 upon p into 1 minus p into 1 upon n1 plus 1 upon n2 whole under square root.
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We have here p1 equal to sample proportion 1 which is x1 upon n1.
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Substituting given values it is 60 divided by 80 which is equal to 0 .75.
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P2 is sample proportion 2 which is x2 upon n2.
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So 40 upon 80, p2 is 0 .5 and p is the pooled proportion.
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It is x1 plus x2 upon n1 plus n2 which we get as 0 .625.
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Substituting values into the formula of z -test statistic, we get z -test statistic value as 3 .266.
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Bit c, p -value...