Concept explainers
A carcinogenicity study was conducted to examine the tumor potential of a drug product scheduled for initial testing in humans. A total of 300 rats (150 males and 150 females) was studied for a 6-month period. At the beginning of the study, 100 rats (50 males. 50 females) were randomly assigned to the control group. 1(H) (50 males. 50 females) to the low-dose group, and the remaining 100 (50 males, 50 females) to the high-dose group. On each day of the 6-month period, the rats in the control group received an injection of an inert solution, whereas those in the drug groups received an injection of the solution plus drug. The sample data are shown in the accompanying table.
- a. Conduct a test of whether there is a significant difference in the proportions of rats having one or more tumors for the three treatment groups with α = .05.
- b. Does there appear to be a drug-related problem regarding tumors for this drug product? That is, as the dose is increased, does there appear to be an increase in the proportion of rats with tumors?
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Chapter 10 Solutions
An Introduction to Statistical Methods and Data Analysis
- An experiment was conducted to assess the efficacy of spraying oats with Malathion (at 0.25 lb/acre) to control the cereal leaf beetle. Twenty farms in southwest Manitoba were used for the study. Ten farms were assigned at random to the control group (no spray) and the other 10 fields were assigned to the treatment group (spray). At the conclusion of the experiment, the number of beetle larvae per square foot was measured at each farm, and a one-tailed test of significance was performed to determine if Malathion reduced the number of beetles. In which one of the following cases would a Type II error occur? (a) We do not conclude malathion is effective when in fact it was effective. (b) We conclude malathion is effective when in fact it is ineffective. (c) We conclude malathion is effective when in fact it is effective. (d) We do not conclude malathion is effective when in fact it is ineffective. (e) We conclude malathion is neither ineffective nor effective.arrow_forwardOne variety of corn is genetically modified to produce chemicals for defense against predators. The standard corn contains the same standard genotype, but without genetic modification for the chemicals. The two types of corn are then planted in randomly placed adjacent plots across a single field. The amount of predators that are present when the corn has matured are then recorded. The data that was recorded of the predators present among each type are listed. Has genetic alterations decreased the amount of predators for the altered genotype? Normality tests for the populations of both contain a p value less than 0.05. The given alpha is 0.05 Modified Corn (20, 18, 26, 23, 17, 23, 22) Standard Corn (89, 64, 102, 96, 56, 77, 84, 59) use an F test to determine if the variance between the 2 lists are different. Based on this result, state the correct 2 sample parametric test to be used. State the null and alternative. Show calculations while rounding to two decimal points.What is the…arrow_forwardIn clinical trails of Nasonex, 3774 adult and adolenscent allergy patients 12 years and older were randomly divided into two groups. The patient in group1 (experimental group) received 200 microgram of Nasonex, while the patient in group 2( control group) receiced a placebo. Of the 2103 patients in the experimental group 547 reported headaches as a side effect. Of the 1671 patients in the control group, 368 reported headaches as a side effect. Determine if the proportion of those taking Nasonex who experienced headaches as a side effect differs from that of those taking the placebo who experienced headaches as a side effect. A) state the null and alternative hypothese: B) construct a 95% confidence interval for the difference between these groups round to 4 places. Intervals: C)using intervals, state conclusion in the language of the problem.arrow_forward
- The impact of a low-calorie diet on laboratory mice's longevity is being investigated by a medical researcher. Twenty mice are split into two groups (E and F) by random. A typical diet is given to Group E, while Group F is given a diet that only contains 70% as many calories as Group E's diet. The length of life (in days) of each mouse over the 36-month trial is documented. Table 2 provides the data that was obtained. The symbol of double star (**) signifies that the mouse was still alive at the end of the investigation. (a) (b) (c) Table 2: The length of life (in days) of each mouse Group E 900 907 751 833 920 787 830 877 848 901 Group F 1037 905 1023 988 1078 1011 ** 1063 898 1033 State a suitable null and alternative hypotheses for the problem. At 5% significance level, test the hypotheses in part (a) by using an appropriate nonparametric test. Write your conclusion.arrow_forwardA test of body reaction to the Malaysian citizens who have taken their vaccine was conducted. Selected citizens who got side effect are categorised according to their blood type and the type of vaccine received. From a sample of 250 citizens, 150 of them were administered withSinovac while the rest received AstraZeneca. Table 4 shows the number of citizens who had side effect after being vaccinated. (Question & Table at images)arrow_forwardA medical student at a community college in city Q wants to study the factors affecting the systolic blood pressure of a person (Y). Generally, the systolic blood pressure depends on the BMI of a person (B) and the age of the person A. She wants to test whether or not the BMI has a significant effect on the systolic blood pressure, keeping the age of the person constant. For her study, she collects a random sample of 150 patients from the city and estimates the following regression function: Y= 15.50 +0.90B + 1.10A. (0.48) (0.35) The test statistic of the study the student wants to conduct (Ho: B, =0 vs. H4: B, #0), keeping other variables constant is. (Round your answer to two decimal places.) At the 5% significance level, the student will v the null hypothesis. Keeping BMI constant, she now wants test whether the age of a person (A) has no significant effect or a positive effect on the person's systolic blood pressure. So, the test statistic associated with the one-sided test the…arrow_forward
- The research and development (R&D) department of a paint manufacturer recently developed a new paint product. The developers are concerned the average area covered per gallon will be less for the new paint than for the existing product. To investigate this concern, the R&D department set up a test in which two random samples of paint were selected. The first sample consisted of 25 one-gallon containers of the company's existing product, and the second of 15 one-gallon containers of the new paint. The statistics shown were computed from eachsample and refer to the number of square feet that each gallon will cover. Based on the sample data, what should the developers conclude using a significance level of 0.05? Assume the populations are normally distributed with equal variances.Current Paint New Paint Current Paint New Paint x1 = Current Paint Column 423 sq. feet x2 = New Paint Column 418 sq feet s1 = 21.7 s2 =…arrow_forwardEighteen middle-aged women with platelet readings between 120,000 platelets per microliter and 150,000 platelets per microliter of blood were selected randomly from the population of similar female patients at a large local hospital. Nine of the 18 women were assigned randomly to group A and received a placebo. The other nine women were assigned to group B and received a new platelet drug. After four months, posttreatment platelet readings were taken for all 18 women and were compared with pretreatment readings. The reduction in platelet level (Pretreatment reading - Posttreatment reading) for each woman in the study is shown here. Group A (placebo) increase (in platelets per microliter): 2,000, 5,000, 7,050, 10,125, 12,345, 17,350, 13,250, 12,200, 9,125 Group B (platelet drug) increase (platelets per microliter): 28,450, 23,438, 36,380, 12,450, 16, 100, 21,350, 39,400, 41,000, 14,325 Create and interpret a 95% confidence interval for the difference in the placebo and the new drug.arrow_forwardA study claims that the combination of vitamin C with vitamin E is more effective for preventing the flu than vitamin C alone. In the study, a group of researchers studied 1132 subjects. The subjects were randomly assigned to out of three study groups. The first group of 310 subjects were instructed to take 600 mg daily of vitamin C. The second group of 418 subjects were instructed to take 600 mg of vitamin C and 200 IU of vitamin E daily. The third group of 404 subjects were instructed to take 600 mg of vitamin C and 400 IU of vitamin E daily. The incidence of flu over a season was recorded. All subjects knew which treatment they were receiving. In this study, which is the control group? O the third group of 404 taking 400 IU of vitamin E O the 1132 subjects O the first group of 310 taking vitamin C alone O the second group of 418 taking 20O IU of vitamin E O There is no control group. This study is O double-blind Onot blind. O not an experiment blind, but not double-blind none of the…arrow_forward
- A study claims that the combination of vitamin C with vitamin E is more effective for preventing the flu than vitamin C alone. In the study, a group of researchers studied 1132 subjects. The subjects were randomly assigned to out of three study groups. The first group of 310 subjects were instructed to take 600 mg daily of vitamin C. The second group of 418 subjects were instructed to take 600 mg of vitamin C and 200 IU of vitamin E daily. The third group of 404 subjects were instructed to take 600 mg of vitamin C and 400 IU of vitamin E daily. The incidence of flu over a season was recorded. All subjects knew which treatment they were receiving.This study is double-blind not an experiment blind, but not double-blind not blind. none of the abovearrow_forwardA study claims that the combination of vitamin C with vitamin E is more effective for preventing the flu than vitamin C alone. In the study, a group of researchers studied 1132 subjects. The subjects were randomly assigned to out of three study groups. The first group of 310 subjects were instructed to take 600 mg daily of vitamin C. The second group of 418 subjects were instructed to take 600 mg of vitamin C and 200 IU of vitamin E daily. The third group of 404 subjects were instructed to take 600 mg of vitamin C and 400 IU of vitamin E daily. The incidence of flu over a season was recorded. All subjects knew which treatment they were receiving.In this study, which is the control group? the second group of 418 taking 200 IU of vitamin E the third group of 404 taking 400 IU of vitamin E the 1132 subjects the first group of 310 taking vitamin C alone There is no control group.arrow_forwardA randomized experiment measured weight gain (in grams) of makes rats under six diets varyingby source of protein (beef, cereal, pork) and level of protein (low, high). Ten rats were assignedto each diet. Outline the design.arrow_forward
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL