Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 11.1, Problem 1E
An experiment was carried out to investigate the effect of species (factor A, with I = 4) and grade (factor B, with J = 3) on breaking strength of wood specimens. One observation was made for each species—grade combination—resulting in SSA = 442.0, SSB = 428.6, and SSE = 123.4. Assume that an additive model is appropriate.
a. Test H0: α1 = α2 = α3 = α4 = 0 (no differences in true average strength due to species) versus Ha: at least one αi ≠ 0 using a level .05 test.
b. Test H0: β1 = β2 = β3 = 0 (no differences in true average strength due to grade) versus Ha: at least one βi ≠ 0 using a level .05 test.
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A laundry detergent company wants to determine if a new formula of detergent, A, cleans better than the original formula, B. Researchers randomly assign 500 pieces of similarly soiled clothes to the two detergents, putting 250 pieces in each group. After washing the clothes, independent reviewers determine the cleanliness of the clothes on a scale of 1–10, with 10 being the cleanest. The researchers calculate the proportion of clothes in each group that receive a rating of 7 or higher. For detergent A, 228 pieces of clothing received a 7 or higher. For detergent B, 210 pieces of clothing received a rating of 7 or higher. Assuming the conditions for inference are met, what is the 90% confidence interval for the difference in proportions of clothes that receive a rating of 7 or higher for the two detergents?
A laundry detergent company wants to determine if a new formula of detergent, A, cleans better than the original formula, B. Researchers randomly assign 500 pieces of similarly soiled clothes to the two detergents, putting 250 pieces in each group. After washing the clothes, independent reviewers determine the cleanliness of the clothes on a scale of 1–10, with 10 being the cleanest. The researchers calculate the proportion of clothes in each group that receive a rating of 7 or higher. For detergent A, 228 pieces of clothing received a 7 or higher. For detergent B, 210 pieces of clothing received a rating of 7 or higher. Assuming the conditions for inference are met, what is the 90% confidence interval for the difference in proportions of clothes that receive a rating of 7 or higher for the two detergents?
Find the z-table here.
A laundry detergent company wants to determine if a new formula of detergent, A, cleans better than the original formula, B. Researchers randomly assign 500 pieces of similarly soiled clothes to the two detergents, putting 250 pieces in each group. After washing the clothes, independent reviewers determine the cleanliness of the clothes on a scale of 1–10, with 10 being the cleanest. The researchers calculate the proportion of clothes in each group that receive a rating of 7 or higher. For detergent A, 228 pieces of clothing received a 7 or higher. For detergent B, 210 pieces of clothing received a rating of 7 or higher.
Based on the 90% confidence interval, (0.02, 0.12), is there convincing evidence that the new formula of laundry detergent is better?
A) There is convincing evidence because the interval is entirely above 0.
B) There is not convincing evidence because the sample sizes are too small.
C) There is convincing evidence because the number of clothing items receiving a…
Chapter 11 Solutions
Probability and Statistics for Engineering and the Sciences
Ch. 11.1 - An experiment was carried out to investigate the...Ch. 11.1 - Four different coatings are being considered for...Ch. 11.1 - Prob. 3ECh. 11.1 - In an experiment to see whether the amount of...Ch. 11.1 - In an experiment to assess the effect of the angle...Ch. 11.1 - A particular county employs three assessors who...Ch. 11.1 - Prob. 7ECh. 11.1 - The paper Exercise Thermoregulation and...Ch. 11.1 - The article The Effects of a Pneumatic Stool and a...Ch. 11.1 - Prob. 10E
Ch. 11.1 - Prob. 11ECh. 11.1 - Prob. 12ECh. 11.1 - Prob. 13ECh. 11.1 - Prob. 14ECh. 11.1 - The power curves of Figures 10.5 and 10.6 can be...Ch. 11.2 - In an experiment to assess the effects of curing...Ch. 11.2 - Prob. 17ECh. 11.2 - The accompanying data resulted from an experiment...Ch. 11.2 - A two-way ANOVA was carried out to assess the...Ch. 11.2 - The article Fatigue Limits of Enamel Bonds with...Ch. 11.2 - In an experiment to investigate the effect of...Ch. 11.2 - Prob. 22ECh. 11.2 - Prob. 23ECh. 11.2 - Prob. 24ECh. 11.2 - Prob. 25ECh. 11.2 - Prob. 26ECh. 11.3 - The output of a continuous extruding machine that...Ch. 11.3 - Prob. 28ECh. 11.3 - Prob. 29ECh. 11.3 - Prob. 30ECh. 11.3 - Nickel titanium (NiTi) shape memory alloy (SMA)...Ch. 11.3 - Prob. 32ECh. 11.3 - Prob. 33ECh. 11.3 - The article The Responsiveness of Food Sales to...Ch. 11.3 - Prob. 35ECh. 11.3 - Prob. 36ECh. 11.3 - Prob. 37ECh. 11.4 - The accompanying data resulted from an experiment...Ch. 11.4 - The accompanying data resulted from a 23...Ch. 11.4 - In a study of processes used to remove impurities...Ch. 11.4 - Prob. 41ECh. 11.4 - Prob. 42ECh. 11.4 - Prob. 43ECh. 11.4 - a. In a 24 experiment, suppose two blocks are to...Ch. 11.4 - a. An experiment was carried out to investigate...Ch. 11.4 - Prob. 46ECh. 11.4 - a. In a seven-factor experiment (A,, G), suppose a...Ch. 11.4 - The article Applying Design of Experiments to...Ch. 11 - The results of a study on the effectiveness of...Ch. 11 - Prob. 51SECh. 11 - Prob. 52SECh. 11 - In an automated chemical coating process, the...Ch. 11 - Coal-fired power plants used in the electrical...Ch. 11 - Impurities in the form of iron oxides lower the...Ch. 11 - Factorial designs have been used in forestry to...Ch. 11 - Prob. 57SECh. 11 - Prob. 58SECh. 11 - The bond strength when mounting an integrated...Ch. 11 - Prob. 60SECh. 11 - Prob. 61SE
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