1. When setting up a hypothesis test regarding two standard deviations or variances, which sample must be sample #1?
2. Give an example of a scatterplot with 5 data points that shows negative linear correlation.
3. The data below represents the prices, in dollars, of a sample of (the same) items at a convenience store and a grocery store.
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Convenience Store
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3.99 5.67 1.92 0.79 3.25 4.19 2.99 5.75 3.99 3.50 2.99 0.99 4.50
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Grocery Store
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3.19 2.99 2.15 1.25 2.50 3.25 2.99 3.95 3.50 2.49 1.99 1.50 3.89
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a. Does the data consist of independent samples or matched pairs?
b. Use your calculator to draw the scatterplot for this data. Sketch what you see here. Does the data appear to be linearly correlated?
3. (Continued) The data below represents the prices, in dollars, of a sample of (the same) items at a convenience store and a grocery store.
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Convenience Store
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3.99 5.67 1.92 0.79 3.25 4.19 2.99 5.75 3.99 3.50 2.99 0.99 4.50
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Grocery Store
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3.19 2.99 2.15 1.25 2.50 3.25 2.99 3.95 3.50 2.49 1.99 1.50 3.89
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c. Is the data significantly linearly correlated? Use your calculator to run the test with .01 significance.
d. What percent of the variation in price at the grocery store is explained by the linear relationship between the stores' prices? Use your results from part (c).
e. Find the 95% prediction interval estimate for the grocery store price of an item that is $4.25 at the convenience store. Use your calculator as much as possible.
f. With .01 significance, test the claim that, on average, there is no difference between the prices of goods at the two stores. Use your calculator.
4. The number of adjectives in samples of poems written by two authors are counted. The results are shown in the table.
a. With .05 significance, test the claim that the standard deviation in number of adjectives is the same for each author. Use the critical value method and a chart.
b. With .05 significance, test the claim that the mean number of adjectives is the same for each author. Use your calculator.
c. Construct a 95% confidence interval estimate for the difference between the mean numbers of adjectives for the two authors. Use formulas and chart.
5. A study compares the conviction rates of two defense attorneys' clients. The results of a sample of trials from each attorney are given below.
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Attorney X
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Attorney Y
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Guilty
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24
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16
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Not Guilty
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58
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16
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a. Use your calculator to construct a 90% confidence interval estimate for the difference in the conviction (guilty) rates for the two attorneys.
b. With .05 significance, test the claim that Attorney X has a lower conviction rate than Attorney Y. Use formulas and chart.