Statistics 215 Lab Winter 2007

For these problems make sure to: (1) Clearly identify the statistical procedure you are using (e.g., matched pairs test, 1-sample z test for a proportion, etc.), (ii) List all assumptions and address whether the statistical inference is appropriate, (iii) Use graphs, tables, and summary statistics, where appropriate; (iv) State your conclusion in context. Adopt a thoughtful and objective tone. Show the relevant printout from your R session.

1. A randomized experiment was performed on mice to determine whether two forms of iron, Fe3+ and Fe4+, are retained differently. If one type is retained especially well, then it may be more useful as a dietary supplement for humans. The mice were given the iron orally. The measurements of interest are the percentages of iron retained in each mouse after a fixed time period had elapsed. The researchers wished to know if there is higher retention for one type than for the other. If so, which type? and by how much? Use graphical and numerical methods to analyze the data. Answer the questions of interest. Make sure to give your answers in a way that will be useful to the researchers.

Fe3+

0.71 1.66 2.01 2.16 2.42 2.42 2.56 2.60 3.31

3.64 3.74 3.74 4.39 4.5 5.07 5.26 8.15 8.24

Fe4+

2.20 2.69 3.54 3.75 3.83 4.08 4.27 4.53 5.32

6.18 6.22 6.33 6.97 6.97 7.52 8.36 11.65 12.45

2. To study the effectiveness of wall insulation in saving energy for home heating, the energy consumption (in MWh) for ten houses in Bristol, England was recorded for two winters; the first winter was before insulation and the second winter was after insulation.

House 1 2 3 4 5 6 7 8 9 10

Before

insulation 12.1 11.0 14.1 13.8 15.5 12.2 12.8 9.9 10.8 12.7

After

insulation 12.0 10.6 13.4 11.2 15.3 13.6 12.6 8.8 9.6 12.4

(a) Discuss whether there is evidence that insulation has reduced the average energy consumption.

(b) Note that this is an observational study, and many factors that could affect the difference are uncontrolled. Name two such factors and indicate how they could have affected the result.

3. The contents of 12 bags of Doritos, all marked with a net weight of 28.3 grams, were checked carefully on a sensitive scale. The recorded weights were

27.8 29.2 28.5 28.7 28.9 29.1 29.5 28.0 28.9 28.4 28.3. 28.1.

Investigate and respond to the company’s stated claim. Give a 90% and 98% confidence interval for the true average net weight. Explain to someone who knows no statistics what your interval means.

4. Advertisements for an instructional video claim that the technique will improve the ability of Little League pitchers to throw strikes, and that, after undergoing the training, players will be able to throw strikes on at least 60% of their pitches. To test this claim, a random sample of 20 Little League pitchers is taken. They throw 50 pitches each, and the number of strikes is recorded. After the players participate in the training program, we repeat the test. The table shows the number of strikes each player threw before and after the training.

Before 28 29 30 32 32 32 32 32 32 33

After 35 36 32 28 30 31 32 34 35 36

Before 33 33 34 34 34 35 36 36 37 37

After 33 35 32 30 33 34 37 33 35 32

(a) Is there evidence that after the training, players can throw strikes more than 60% of the time?

(b) Is there evidence that the training is effective in improving a player’s ability to throw strikes?