a. In a 24 experiment, suppose two blocks are to be used, and it is decided to confound the ABCD interaction with the block effect. Which treatments should be carried out in the first block [the one containing the treatment (1)], and which treatments are allocated to the second block?
b. In an experiment to investigate niacin retention in vegetables as a
Treatment | xijkl | Treatment | xijkl |
(1) | 91 | d | 72 |
a | 85 | ad | 78 |
b | 92 | bd | 68 |
ab | 94 | abd | 79 |
c | 86 | cd | 69 |
ac | 83 | acd | 75 |
bc | 85 | bcd | 72 |
abc | 90 | abcd | 71 |
c. Assume that all three-way interaction effects are absent, so that the associated sums of squares can be combined to yield an estimate of σ2, and carry out all appropriate tests at level .05.
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Chapter 11 Solutions
Probability and Statistics for Engineering and the Sciences
- a) Three samples of five mice were randomly selected to be placed in a standard maze but with different door colours (red, green, black). The time (in seconds) required to complete the maze was recorded as in Table 1. Table 1: Time to Complete the Maze Color Time Red 9. 11 10 9 15 Green 20 21 23 17 Black 8 14 7 (i) Identify the dependent and independent variables. (ii) How many treatments involved in this study? (iii) How many replications for each treatment?arrow_forward14.33 A preservative was added to fresh and wilted alfalfa silage (Snedecor 1948). The lactic acid concentration was measured at five periods after ensiling began. There were two replications. The results are given in Table 14.6. Let factor A be condition (fresh or wilted) and factor B be period. Test for main effects and interactions. TABLE 14.6 Lactic Acid" at Five Successive Time Periods for Fresh and Wilted Alfalfa Silage Condition Fresh Wilted "In mg/g of silage 1 13.4 16.0 14.4 20.0 2 37.5 42.7 29.3 34.5 Period 3 65.2 54.9 36.4 39.7 4 PROBLEMS 60.8 57.1 39.1 38.7 5 37.7 49.2 39.4 39.7 411arrow_forwardA physiologist has conducted an experiment to evaluate the effect of hormone X on sexual behavior. Ten rats were injected with hormone X and 10 other rats received a placebo injection. The number of matings was counted over a 20-minute period. The results are shown in the table below. Table 1: Data from hormone X experiment Group 1 Hormone X Group 2 Placebo X1 (X1) 2 X2 (X1) 2 8 64 5 25 10 100 6 36 12 144 3 9 6 36 4 16 6 36 7 49 7 49 8 64 9 81 6 36 8 64 5 25 7 49 4 16 11 121 8 64 84 744 56 340 a) What is the alternative hypothesis? Use a nondirectional hypothesis. b) What is the null hypothesis? c) What do you conclude? Use α = 0.05 (2-tail)arrow_forward
- A random sample of 1000 people with known allergies to poison ivy participated in a recent study. Oil from the poison ivy plant was rubbed on a patch of skin. For 500 of the subjects, the oil it was washed off within 5 minutes. For the other 500 subjects, the oil was washed off after 5 minutes. Observed reactions were recorded as "none," "mild," or "strong." The results are summarized in the following table. Reaction Within 5 Minutes After 5 Minutes Row Total NoneMildStrong 4056530 48326126 453391156 Column Total 500 500 1000 Suppose a person selected at random from this sample of 1000 subjects. What is the probability that a strong reaction was observed, given that the oil was washed off within 5 minutes?arrow_forward1. Does the herb Echinacea help the common cold? A study investigated the impact of echinacea vs. a standard cold medication on cold symptoms. Each subject in the study chose to take either the echinacea or a standard cold medication in capsule form After taking the capsule for one week, the subjects then reported to the researchers the status of their cold symptoms. The researchers subsequently reported that there was no statistically significant difference in the duration of the cold between these groups. The variable duration of cold in this study would be the a) Explanatory variable b) Response variable c) Population d) Statisticarrow_forwardQUESTION 7 Problem 11.57ea: Provide a point estimate for the SE standard error of the regression. Use 3 decimals in your answer Hint: L-23: p 15 (Ex. 11.3dd)arrow_forward
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- A researcher conducts an independent-measures, two factor study with two levels of factor A and two levels of factor B, using a sample of n = 8 participants in each treatment condition. a. What are the df values for the F-ratio evaluating the main effect of factor A? b. What are the df values for the F-ratio evaluating the main effect of factor B? c. What are the df values for the F-ratio evaluating the interaction?arrow_forwardQ 1.8: Four testing agencies are going to test whether a medication causes nausea in patients. All agencies reported high rates of nausea in patients using the medication. The method of each agency is described below. Select the agency that could claim that the medication causes nausea based on their method. A : The fourth agency brings volunteers currently using the medication to a facility and randomly gives half of participants the medication and half a placebo. They tell the patients that they are collecting data on all effects of the medication. B : The second agency sends a representative to the homes of existing patients to inquire about their appetite since they started taking the medication. C : The third agency brings volunteers currently using the medication to a clinical facility to observe their eating habits and tells the volunteers they are being observed for nausea. D : The first agency sends a questionnaire to existing…arrow_forwardRed Wine and Weight LossResveratrol, a compound in grapes and red wine, has been shown to promote weight loss in rodents and now in a primate.1 Lemurs fed a resveratrol supplement for four weeks had decreased food intake, increased metabolic rate, and a reduction in seasonal body-mass gain compared to a control group. Suppose a hypothetical study is done for a different primate species, with one group given a resveratrol supplement and the other group given a placebo. We wish to see if there is evidence that resveratrol increases the mean metabolism rate for this species. (This exercise presents hypothetical data. We will see the results from the actual study later in this chapter.) (a) State the null and alternative hypotheses.Let group 1 be the species taking a resveratrol supplement and let group 2 be the species taking a placebo.arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,