Phase I of a Clinical Trial A clinical test on humans of a new drug is normally done in three phases. Phase I is conducted with a relatively small number of healthy volunteers. For example, a phase I test of bexarotene involved only 14 subjects. Assume that we want to treat 14 healthy humans with this new drug and we have 16 suitable volunteers available.
a. If the subjects are selected and treated one at a time in sequence, how many different sequential arrangements are possible if 14 people are selected from the 16 that are available?
b. If 14 subjects are selected from the 16 that are available, and the 14 selected subjects are all treated at the same time, how many different treatment groups are possible?
c. If 14 subjects are randomly selected and treated at the same time, what is the
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Chapter 4 Solutions
Elementary Statistics (13th Edition)
- Urban Travel Times Population of cities and driving times are related, as shown in the accompanying table, which shows the 1960 population N, in thousands, for several cities, together with the average time T, in minutes, sent by residents driving to work. City Population N Driving time T Los Angeles 6489 16.8 Pittsburgh 1804 12.6 Washington 1808 14.3 Hutchinson 38 6.1 Nashville 347 10.8 Tallahassee 48 7.3 An analysis of these data, along with data from 17 other cities in the United States and Canada, led to a power model of average driving time as a function of population. a Construct a power model of driving time in minutes as a function of population measured in thousands b Is average driving time in Pittsburgh more or less than would be expected from its population? c If you wish to move to a smaller city to reduce your average driving time to work by 25, how much smaller should the city be?arrow_forward1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.6. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.6 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 1 Food C 1 1 2arrow_forwardCustomer Preference Two movie theatres that show several different movies each night compete for the same audience. Of the people who attend theatre A one night, 10 will attend again the next night and 5 will attend Theatre B the next night. Of the people who attend Theatre B one night, 8 will attend again the next night and 6 will attend Theatre A the next night. Of the people who attend neither theatre one night, 3 will attend Theatre A the next night and 4 will attend Theatre B the next night. Find and interpret the steady state matrix for this situation.arrow_forward
- Do lizards play a role in spreading plant seeds? Some research carried out in a country would suggest so. The researchers collected 400 seeds of this particular type of fig, 100 of which were from each treatment: lizard dung, bird dung, rock hyrax dung, and uneaten figs. They planted these seeds in batches of 5, and for each group of 5 they recorded how many of the seeds germinated. This resulted in 20 observations for each treatment. The treatment means and standard deviations are given in the accompanying table. Treatment n Uneaten figs 20 | 2.80 0.30 Lizard dung 20 2.75 0.36 Bird dung 20 2.10 0.35 Hyrax dung 20 1.85 0.29 n USE SALT (a) Construct the appropriate ANOVA table, and test the hypothesis that there is no difference between the means for the number of seeds germinating for the four treatments. (Use a = 0.05. Round your mean squares to three decimal places and F statistic to two decimal places.) Source of Variation Sum of Squares Mean df F Square Treatments 3 13.45 4.483333…arrow_forwardDo lizards play a role in spreading plant seeds? Some research carried out in a country would suggest so. The researchers collected 400 seeds of this particular type of fig, 100 of which were from each treatment: lizard dung, bird dung, rock hyrax dung, and uneaten figs. They planted these seeds in batches of 5, and for each group of 5 they recorded how many of the seeds germinated. This resulted in 20 observations for each treatment. The treatment means and standard deviations are given in the accompanying table. Treatment x S Uneaten figs 20 2.80 0.30 Lizard dung 20 2.75 0.36 Bird dung 20 2.10 0.35 Hyrax dung 20 1.85 0.29 USE SALT (a) Construct the appropriate ANOVA table, and test the hypothesis that there is no difference between the means for the number of seeds germinating for the four treatments. (Use a = 0.05. Round your mean squares to three decimal places and F statistic to two decimal places.) Source of df Sum of Squares Mean Square F Variation Treatments Error Total Use…arrow_forwardOne of the markers of toxicity of a proposed drug during drug development is loss of weight in the exposed individuals. Female was exposed to a proposed drug and the effects were observed during a 28 days period. Another record only the vehicle. These two groups were animals of similar age and gender and were all treated in similar ways regarding nutrition, water and environment. Result of the weight of 16 male mice before and after treatment are tabulated in table 2 below: Table 2: Table of the weights (gm) of 16 male mice before (X1a) and after treatment (X1b) X1a 20 21.2 20.6 19.5 18.9 20.2 21 19.6 17.8 18.5 18.3 19.2 19.6 19.4 19.2 19 X1b 20.9 21.9 21.2 21 19.9 20.9 21.8 21 18.6 19.9 19 20 20.1 20 20 20.7 Determine if these was a statistical weight difference (gain/loss in the 2 groups) Using paired t-testarrow_forward
- Do lizards play a role in spreading plant seeds? Some research carried out in South Africa would suggest so. Researchers on a study collected 400 seeds of a particular type of fig, 100 of which were from each treatment: lizard dung, bird dung, rock hyrax dung, and uneaten figs. They planted these seeds in batches of 5, and for each group of 5 they recorded how many of the seeds germinated. This resulted in 20 observations for each treatment. The treatment means and standard deviations are given in the accompanying table. Treatment n x s Uneaten figs 20 2.50 0.30 Lizard dung 20 2.30 0.33 Bird dung 20 1.70 0.34 Hyrax dung 20 1.45 0.28 (a) Construct the appropriate ANOVA table. (Use technology. Round your answers to three decimal places.) Source ofvariation Degrees offreedom Sum ofsquares Meansquares F Ratio F Prob Between Groups Within Group Total 79 Test the hypothesis that there is no difference between mean number of seeds…arrow_forwardDo lizards play a role in spreading plant seeds? Some research carried out in South Africa would suggest so. Researchers on a study collected 400 seeds of a particular type of fig, 100 of which were from each treatment: lizard dung, bird dung, rock hyrax dung, and uneaten figs. They planted these seeds in batches of 5, and for each group of 5 they recorded how many of the seeds germinated. This resulted in 20 observations for each treatment. The treatment means and standard deviations are given in the accompanying table. Treatment Uneaten figs 20 2.50 0.29 Lizard dung 20 2.40 0.32 Bird dung 20 1.80 0.35 Hyrax dung 20 1.40 0.29 (a) Construct the appropriate ANOVA table. (Use technology. Round your answers to three decimal places.) Degrees of freedom Source of Sum of Mean F Ratio F Prob variation squares squares Between Groups Within Group Total 79 Test the hypothesis that there is no difference between mean number of seeds germinating for the four treatments. (Use a significance level…arrow_forwardA pharmaceutical company conducts an experiment to test the effect of a new cholesterol medication. The company selects 15 subjects randomly from a larger population. Each subject is randomly assigned to one of three treatment groups. Within each treament group, subjects receive a different dose of the new medication. In Group 1, subjects receive 0 mg/day; in Group 2, 50 mg/day; and in Group 3, 100 mg/day. What test would you use?arrow_forward
- c) A pharmaceutical company conducts an experiment to test the effect of a new cholesterol medication. The company selects 15 subjects randomly from a larger population. Each subject is randomly assigned to one of three treatment groups. Within each treatment group, subjects receive a different dose of the new medication. In Group 1, subjects receive 0 mg/day; in Group 2, 50 mg/day; and in Group 3, 100 mg/day. At a=0.05 does dosage level have a significant effect on cholesterol level? Group 1 (0 mg): 210, 240, 270, 270,300 Group 2 (50mg): 210, 240, 240, 270,270 Group 3 (100mg): 180, 210, 210, 210,240arrow_forwardHurricane damage: In August and September 2005 , Hurricanes Katrina and Rita caused extraordinary flooding in New Orleans, Louisiana. Many homes were severely damaged or destroyed, and of those that survived, many required extensive cleaning. It was thought that cleaning flood-damaged homes might present a health hazard due to the large amounts of mold present in many of the homes. In a sample of 370 residents of Orleans Parish who had participated in the cleaning of one or more homes, 65 had experienced symptoms of wheezing, and in a sample of 173 residents who had not participated in the cleaning, 22 reported wheezing symptoms (numbers read from a graph). Can you conclude that the proportion of residents with wheezing symptoms is greater among those who participated in the cleaning of flood-damaged homes? Let p1 denote the proportion of residents with wheezing symptoms who had cleaned flood-damaged homes and p2 denote the proportion of residents with wheezing symptoms…arrow_forwardSubject: stetarrow_forward
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