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The two-stage model of carcinogenesis is based on the premise that for a cancer to develop, a normal cell must first undergo a “first hit” and mutate to become a susceptible or intermediate cell. An intermediate cell then must undergo a “second hit” and mutate to become a malignant cell. A cancer develops if at least one cell becomes a malignant cell. This model has been applied to the development of breast cancer in females (Moolgavkar et al. [15]).
Suppose there are 108 normal breast cells and 0 intermediate or malignant breast cells among 20-year-old females. The probability that a normal breast cell will mutate to become an intermediate cell is 10−7 per year.
Suppose a woman has 300 intermediate cells by age 45. What is the probability that she develops breast cancer by age 46? By age 50? (Hint: Use the Poisson approximation to the binomial distribution.)
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EBK FUNDAMENTALS OF BIOSTATISTICS
- A number of studies have examined how alcohol consumption affects neuroticism using an animal model. Two kittens are randomly selected from each of 7 litters (two cats from each litter). One cat from each pair is assigned to the experimental group which is subjected to a procedure that induces temporary neurosis. The other cat from each pair is part of the control group (no neurosis induction). All the cats are then offered milk spiked with 5% alcohol. The amount of milk consumed in three minutes is measured (in milliliters). Do the kittens in the experimental group drink more alcohol than the kittens in the control group? what statistical test should be used and why?arrow_forwardA number of studies have examined how alcohol consumption affects neuroticism using an animal model. Two kittens are randomly selected from each of 7 litters (two cats from each litter). One cat from each pair is assigned to the experimental group which is subjected to a procedure that induces temporary neurosis. The other cat from each pair is part of the control group (no neurosis induction). All the cats are then offered milk spiked with 5% alcohol. The amount of milk consumed in three minutes is measured (in milliliters). Do the kittens in the experimental group drink more alcohol than the kittens in the control group? What test should you use and why?arrow_forwardThe recessive mutation bg (beige) in mice results in a decrease in the activity of natural killer cells in homozygous mutant mice. You test the hypothesis that this cell type plays an important role in rejection of tumor cells (derived from a tumor induced in an isogenic animal) by injecting animals with genotypes bg/bg or bg/+ with 106 cells and measuring the time required for the development of a palpable tumor in each animal. You obtain the following data: Time to tumor development (days) Genotype 28, 51, 47, 80 14, 35, 17, 37, 16 3. What is the most appropriate statistical approach to test the hypothesis? a. t-test for paired samples b. t-test for unpaired samples C. ANOVA d. Mann-Whitney U test e. Kruskal-Wallis test 4. Is there a significant difference in tumor latency between the two groups? bg/+ bg/bgarrow_forward
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- One 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_forwardThe Diabetes Control and Complications trial research group, randomly assigned volunteers with type 1 (insulin-dependent) diabetes mellitus, but without retinopathy, either to a conventional treatment or to a more intensive treatment aimed at maintaining normal blood glucose levels. The volunteers' health was monitored closely for approximately six years. By the end of the study, 91 patients out of 378 in the conventional treatment group had developed retinopathy, whereas 23 out of 348 in the intensive treatment group had developed retinopathy. Test whether the rates of retinopathy differed significantly between the two treatment groups, if they did, which rate was significantly lower. 1. Provide the null hypothesis 2. Provide the alternative hypotheses 3. calculate the appropriate test statistic. Show all work 4. Identify the p-value for that test statistic 5. Using the p-value method and an alpha level of 0.02 state what your conclusions are regarding the null hypothesis, and…arrow_forwardThe Diabetes Control and Complications trial research group, randomly assigned volunteers with type 1 (insulin-dependent) diabetes mellitus, but without retinopathy, either to a conventional treatment or to a more intensive treatment aimed at maintaining normal blood glucose levels. The volunteers' health was monitored closely for approximately six years. By the end of the study, 91 patients out of 378 in the conventional treatment group had developed retinopathy, whereas 23 out of 348 in the intensive treatment group had developed retinopathy. Test wether the rates of retionpathy differed significantly betweenthe two treatment groups, if they did, which rate was significantly lower. 1. Provide the null hypothesis 2. Provide the alternative hypotheses 3. calculate the appropriate test statistic. Show all work 4. Indentify the p-value for that test statistic 5. Using the p-vlaue method and an alpha level of 0.02 state what your conclusions is regarding the null hypothesis, and…arrow_forward
- Calcium is the most abundant mineral in the human body and has several important functions. Most of the body calcium is stored in the bones and teeth, where it functions to support their structure. Recommendations for calcium are provided in Dietary Reference Intakes, developed by the Institute of Medicine of the National Academy of Sciences. The recommended adequate intake (RAI) for calcium for adults (ages 19-50) is 1000 mg per day. A random sample of 18 adults with incomes below the poverty level gave the following calcium intakes:886 633 943 847 934 8411193 820 774 834 1050 10581192 975 1313 872 1079 809Assume the population standard deviation for daily calcium intake for adults with incomes below the poverty level is 188mg.At the 0.05 level of significance, does the data provided above provide evidence to suggest that the mean calcium intake of all adults with incomes below the poverty level is less than the RAI pf 1000mg per day? Step 1: Define the parameter & setup the…arrow_forwardMost cases of cervical cancer are linked to a few strains of the human papilloma virus (HPV). The pharmaceutical company Merck developed a vaccine (Gardisil) against these HPV strains. Worldwide clinical trials followed young women after vaccination or administration of placebo for two to four years for signs of HPV-caused cervical cancer. Based on a sample of 100 women in the Gardisil group, 34 % developed cervical cancer, and based on a sample of 100 women in the placebo group, 44 % developed cervical cancer. Test the claim that the proportion of women who developed cervical cancer in the Gardisil group is less than the proportion of women who developed cervical cancer in the placebo group at a = 0.05. Round your answers to three decimal places, and round any interim calculations to four decimal places. Fill in the hypotheses below where p₁ denotes the proportion of women who developed cervical cancer in the Gardisil group and p2 denotes the proportion of women who developed cervical…arrow_forwardMost cases of cervical cancer are linked to a few strains of the human papilloma virus (HPV). The pharmaceutical company Merck developed a vaccine (Gardisil) against these HPV strains. Worldwide clinical trials followed young women after vaccination or administration of placebo for two to four years for signs of HPV-caused cervical cancer. Based on a sample of 100 women in the Gardisil group, 34 % developed cervical cancer, and based on a sample of 100 women in the placebo group, 44% developed cervical cancer. Test the claim that the proportion of women who developed cervical cancer in the Gardisil group is less than the proportion of women who developed cervical cancer in the placebo group at a = 0.05. Round your answers to three decimal places, and round any interim calculations to four decimal places. Fill in the hypotheses below where p₁ denotes the proportion of women who developed cervical cancer in the Gardisil group and p2 denotes the proportion of women who developed cervical…arrow_forward
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