invest_3ed.pdf

# Twins were found in a search through the united

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twins were found in a search through the United States and Canada, the ages ranged from 25 to 44 years, with 8 male and 7 female pairs. The data (in cubic centimeters) for the left hippocampus region of the brain are in hippocampus.txt . The primary research question is whether the data provide evidence of a difference in hippocampus volumes between those affected by schizophrenia and those unaffected. (a) Calculate the difference in hippocampus volumes for each pair of twins (unaffected ± affected). (b) Calculate and interpret a 95% confidence interval for the mean volume difference using the paired t- interval. Also comment on the validity of this procedure. (c) Based on this confidence interval, is there statistically significant evidence that the mean difference in left hippocampus volumes is different from zero? Explain. Investigation 4.10: Comparison Shopping In 1999, student group at Cal Poly carried out a study to compare the prices at two different local grocery stores. The inventory list for Scolari’s (a privately -owned local store) was broken into 32 sheets, each with 30 items. A number between 01 and 30 was randomly generated, 17, and the 17 th item on each sheet was selected. Each student was then responsible for obtaining the price of that item at both Scolari’s and Lucky’s (which advertises itself as a discount grocery store) . If the exact item was not available at both stores, the item was adjusted slightly (size or brand name) so that the identical item could be priced at both stores. Students at Cal Poly gathered two prices for a set of 29 items. The data are available in shopping99.txt . (a) Identify the observational units, response variable, population, and sample in this study. Which store do you suspect will have lower prices? Observational units: Response variable: Population: Sample: Initial conjecture: (b) Was this an experimental study or an observational study? Was this a simple random sample? Was it a probability sample? What is the advantage of this procedure over a simple random sample? Are there any disadvantages in selecting the sample this way?

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Chance/Rossman, 2015 ISCAM III Investigation 4.10 298 (c) Did these students use independent samples or a paired design to collect their data? (d) Define the parameter of interest and state the null and alternative hypotheses corresponding to your initial conjecture. Descriptive statistics for the items’ prices (in dollars) at each store, and for the differences in prices, as well as a dotplot of the differences are shown here: Variable N Mean StDev Minimum Q1 Median Q3 Maximum Luckys 31 2.408 1.660 0.490 1.090 1.990 2.790 6.990 Scolaris 29 2.593 1.742 0.500 1.020 2.300 3.585 6.790 diffs 29 -0.1566 0.4083 -1.2300 -0.3250 0.0000 0.1000 0.7600 After further investigation on the outliers, only the milk was found to be recorded incorrectly, two different sizes, and it was removed from the data set.
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