7 - Boxplot of midterm 40 Histogram of midterm 30 50 60 70...

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100 90 80 70 60 50 40 30 midterm Boxplot of midterm 100 80 60 40 20 0 40 30 20 10 0 midt erm Frequency Histogram of midterm mean 76.64 median 80 minimum 31 Q1 70 Q3 87 maximum 96
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1 STAT E-50 - Introduction to Statistics Testing Hypotheses About Proportions Hypotheses ± The null hypothesis: H 0 : parameter = hypothesized value ± The alternative hypothesis: H a : parameter = value we would accept if we reject the null hypothesis
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2 STAT E-50 - Introduction to Statistics Testing Hypotheses About Proportions Hypotheses ± The null hypothesis: H 0 : parameter = hypothesized value ± The alternative hypothesis: H a : parameter = value we would accept if we reject the null hypothesis H 0 : p = .4 or H 0 : p = .25 or H 0 : p = .53 H a : p > .4 H a : p < .25 H a : p .53
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3 Model ± Specify the model you will use to test the null hypothesis ± State the parameter of interest ± List the assumptions and check the conditions ± Name the statistical test you will use
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4 Mechanics ± Calculate a test statistic from the data. ± Obtain a P-value = the probability that the observed value of the test statistic (or a more extreme value) could occur if the null model were correct. ± If the P-value is small enough, we will reject the null hypothesis.
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5 Conclusion ± Statistical conclusion: state whether you reject or fail to reject the null hypothesis ± State your conclusion in context
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One-proportion z-test H 0 : p = p 0 Test statistic is 0 ˆ pp z ˆ SD(p) = where 00 pq ˆ SD(p) n = When the conditions are met and the null hypothesis is true, this statistic follows the standard Normal model. Conditions: Independence condition Random sampling condition 10% condition Success/failure condition (using p 0 and q 0 ) Note: p 0 is the value you are testing in H 0 ; q 0 = 1 - p 0 p is the observed value of p ˆ 6
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7 1. An American Demographics study conducted in 1980 found that 40% of new car buyers were women. Suppose that in a random sample of 120 new car buyers in 2000, 57 were women. Does this indicate that the true proportion of new car buyers in 2000 who were women is significantly larger than the 1980 proportion? Plan What do we want to know? What are the variables? What are the W’s?
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8 1. An American Demographics study conducted in 1980 found that 40% of new car buyers were women. Suppose that in a random sample of 120 new car buyers in 2000, 57 were women. Does this indicate that the true proportion of new car buyers in 2000 who were women is significantly larger than the 1980 proportion? Plan What do we want to know? We want to know whether the proportion of new car buyers in 2000 who were women is greater than 40%, which was the proportion in 1980. What are the variables? What are the W’s? The data is the genders of new car buyers in a sample of 120 new car buyers in 2000. The parameter of interest is the proportion of female car buyers.
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10 Hypotheses H 0 : p = .40 H a : p > .40
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11 1. An American Demographics study conducted in 1980 found that 40% of new car buyers were women. Suppose that in a random sample of 120 new car buyers in 2000, 57 were women. Does this indicate that the true proportion of new car buyers in 2000 who were women is significantly larger than the 1980 proportion?
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This note was uploaded on 05/20/2008 for the course STAT 50 taught by Professor Weinstein during the Spring '08 term at Harvard.

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7 - Boxplot of midterm 40 Histogram of midterm 30 50 60 70...

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