Question 1132704
a) sample proportion of yellow peas = 159/(420+159) = 0.275
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standard error = square root(0.275*(1=0.275)/(420+159)) = 0.019
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alpha(a) = 1 -(90/100) = 0.10
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critical probability(p*) = 1 -(a/2) = 0.95
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I assume the population is normally distributed and since the sample is > 30, a normal distribution is used to construct the 90% confidence interval
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The z-score associated with p* is 1.645, which is the critical value(CV)
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Margin of error = CV * SE = 1.645 * 0.019 = 0.031
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90% confidence interval is 0.275 + or - 0.031, (0.244, 0.306)
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b)  The 90% confidence level means that we would expect 90% of the confidence interval estimates to include the population proportion for yellow peas.
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Ho: X = 0.25
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H1: X not = 0.25
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Ho is our null hypothesis and H1 implies a two-tailed test
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z = (0.275-0.25)/0.019 = 1.316
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since this is a two-tailed test, we reject Ho if 1.316 > 1.96 or if 1.316 < -1.96, since 1.316 < 1.96 we do not reject Ho
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