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Week_12_Practice_Problem_Solutions

# Week_12_Practice_Problem_Solutions - Week 12 Practice...

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Unformatted text preview: Week 12 Practice Problems Solution 1. Formaldehyde is a gas to which some individuals have an allergic reaction. To see if UFFI (a type of insulation) is a significant source of formaldehyde in homes in Canada, 25 homes with UFFI were selected at random from a list of homes that had received a grant from the Federal Government to pay (in part) for the insulation. For each selected home, researchers chose another house located nearby and of the same age that did not have UFFI installed. Then the formaldehyde concentration (in parts per billion) was measured in each selected house. The data and some summaries are pair UFFI Control difference pair UFFI Control difference 1 44.3 44.2 0.1 14 57.7 55.1 2.6 2 55.3 54.9 0.4 15 51 52 -1 3 37.7 32.1 5.6 16 42.2 40.4 1.8 4 46 47 -1 17 51.7 47.5 4.2 5 42.7 42.5 0.2 18 47.1 45.4 1.7 6 57.4 52.3 5.1 19 49.6 49.5 0.1 7 44.3 44.2 0.1 20 52 48.9 3.1 8 45.7 39.3 6.4 21 56 53.3 2.7 9 58.2 55.2 3 22 51.5 45 6.5 10 37.5 36.2 1.3 23 53.5 48.8 4.7 11 40.6 34.8 5.8 24 59.7 54.2 5.5 12 55.7 53.8 1.9 25 54.8 51.3 3.5 13 51.9 52.4 -0.5 average 49.76 47.21 2.55 sd 6.58 6.7 2.42 a) Is this an experimental or observational plan? Explain. This is an observational plan because it does not manipulate any explanatory variate in the sample. It just simply measures the variate on each sample unit. b) What is the advantage of selecting the homes in pairs? Pairing reduces the risk of confounding. We model the differences 1 2 { ,..., } 5 y y because we suspect that homes within each pair will be more alike than homes in different pairs. We have , ~ (0, ), 1,...25, i i i Y R R G i independent μ σ = + = c) What does the parameter μ represent? μ represents the overall mean of formaldehyde concentration difference within each pairs in the study population (all pairs in the database) d) Is there any evidence that μ is different from 0? Suppose μ = 0. The estimates of the parameters are ˆ μ = 2.55, ˆ σ = 2.42 The discrepancy measure is d = ˆ μ − ˆ σ / 25 = 5.269 P ( D ≥ d ) = P ( t 24 ≥ 5.269) ≈ 0 There is strong evidence against the hypothesis that μ = 0. e) Can you conclude that UFFI is a significant health hazard? No. First there is the risk of confounding; some lurking explanatory variate may explain the observed significant difference. And second, there is nothing in the study that connects the higher formaldehyde level and health. f) Why is an experimental plan difficult in this context? Because we cannot change whether or not any house has UFFI. 2. In a survey of small to medium enterprises (SMEs) in Canada, 100 companies were asked a series of questions about their recent spending on technology and also their profitability (as a percent of sales). The goal of the study was to determine if increased spending on technology produced increased profits. A scatterplot of the data and some summaries are shown below. scatterplot of the data and some summaries are shown below....
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Week_12_Practice_Problem_Solutions - Week 12 Practice...

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