A farmer is testing the effects of 4 different fertilizers on the yields of a certain variety of tomato plants. The four fertilizers are applied to each of 5 different tomato plants and the numbers of tomatoes produced by each plant are recorded. The table below shows the results: Fertilizer A Fertilizer B Fertilizer C Fertilizer D Mean 34.6 20.2 34.6 31.6 Standard 3.8 4.0 4.7 2.3 deviation An ANOVA test is to be done, using a significance level of 0.05 A. How many degrees of freedom are there for the numerator?
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- A team of researchers working on the development of vaccines conducted a study on two vaccines. Thirty individuals participated in the study and were randomly assigned to two groups and one group received vaccine 1 and the other group vaccine 2. The researchers then measured the amount of antibody in the individuals' blood after ingestion, entered R and calculated some fish sizes that can be seen here below. x̄1 = 494,54, s1 =52,39, x̄2 = 467,93, s2 = 45,20, d = 26,61, sd = 68,69. Blood levels of antibodies can be expected to follow normal distribution. Use α = 0,05. a) What is the value of the test size to check if there is a difference in the distribution of antibody levels for the two drugs?b) What is the value of the test size to check if there is a difference in the mean amount of antibody in the blood after taking the two vaccines?c) What conclusion do you draw from the hypothesis test in point b about the possible difference in the mean amount of antibody after oral…A 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…A team of researchers working on the development of vaccines conducted a study on two vaccines. Thirty individuals participated in the study and were randomly assigned to two groups and one group received vaccine 1 and the other group vaccine 2. The researchers then measured the amount of antibody in the individuals' blood after ingestion, entered R and calculated some fish sizes that can be seen here below. x̄1 = 494,54, s1 =52,39, x̄2 = 467,93, s2 = 45,20, d = 26,61, sd = 68,69. Blood levels of antibodies can be expected to follow normal distribution. Use α = 0,05. c) What conclusion do you draw from the hypothesis test in point b about the possible difference in the mean amount of antibody after oral administration of the vaccines? d) The researchers also created a 95% confidence interval for the difference between the averages. Will the confidence interval contain the value 0? Justify your answer without calculating the confidence interval.e) Let us now assume that there is in fact…
- Biologists in Minnesota are interested in determining if there is a difference in the invasion rate of Asian Carp (which can be detrimental to the environment) between the Mississippi River and Lake Mille Lacs. In the Mississippi River, it was found that 206 of 579 fish caught were Asian Carp. In Lake Mille Lacs, 28 of 132 fish caught were Asian Carp. Let p, = the true proportion of Asian Carp in the Mississippi River and let p2 = the true proportion of Asian Carp in Lake Mille Lacs. A test of Ho: P₁ = P2 vs. Ha: P₁ P₂ resulted in a p-value of 0.0015. Which of the following is a correct conclusion? (A) The test is not appropriate, since the researchers should have conducted a one-sided test. (B) The test is not appropriate, since the sample size is too small to conduct an inference test for proportions. (C) The test is not appropriate, since the two sample sizes are very different. (D) The p-value of this test is large, indicating we have sufficient evidence to conclude that a…A company is testing a new drug and wants to determine what is the most effective dose in reducing the size of cancerous tumors. The company randomly select a sample of 32 individuals and randomly assigns them into 4 groups of 8 each. One group get 5mg of drug x, a second group get 10mg, a third group gets 15 mg, and the fourth group gets 20mg. After two months the company finds the average size of the tumors to be 40mm, 37mm, 26mm, and 12mm for each group, respectively. (1) State the null and alternative hypotheses for this study (2) What is the dependent and independent variable for this study (3) What test statistic/hypothesis test would you select to determine if the means are significantly difference at the alpha .05 level? (4) What critical value would you use to make your decision to reject or retain the null hypothesis at alpha .05?In an effort to link cold environments with hypertension in humans, a preliminary experiment was conducted to investigate the effect of cold on hypertension in rats. Two random samples of 6 rats each were exposed to different environments. One sample of rats was held in a normal environment at 26°C. The other sample was held in a cold 5°C environment. Blood pressures and heart rates were measured for rats for both groups. The blood pressures for the 12 rats are shown in the table below. a. Provide a 95% confidence interval on the difference in the two population meansb. Do the data provide sufficient evidence that rats exposed to a 5°C environment have a higher mean blood pressure than rats exposed to a 26°C environment? Use α = 0.05
- A farmer would like to investigate the relationship between the obtained yield of apple trees and the amount of weeds found in their roots. For this reason, nine apple trees of the same type were randomly selected and the amount of weeds in their roots (x grams) was recorded together with their yield (y kilograms). Year #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 Weeds in roots (x) 30 28 32 25 25 24 22 24 35 40 Yield (y) 25 30 27 40 42 41 50 45 30 25 Draw a scatter diagram of these data. Label the diagram carefully. Calculate the sample correlation coefficient. Interpret your findings. Calculate the least squares line of y on x and draw the line on the scatter diagram. Based on the regression equation in part (iii.), what will be the predicted yield of apple for a tree with 37 grams of weeds in its roots? Will you trust this value? Justify your answer. Briefly comment on…Many young men in North America and Europe (but not in Asia) tend to think they need more muscle to be attractive. One study presented 200 young American men with 100 images of men with various levels of muscle. Researchers measure level of muscle in kilograms of fat‑free body mass per square meter of body surface area (kg/m2). Typical young men have about 20 kg/m2.. Each subject chose two images, one that represented his own level of body muscle and one that he thought represented "what women prefer." The mean gap between self‑image and "what women prefer" was 2.35 kg/m2.. Suppose that the "muscle gap" in the population of all young men has a Normal distribution with standard deviation 2.5 kg/m2.. If young men thought that their own level of muscle was about what women prefer, the mean "muscle gap" in the study would be 0. We suspect (before seeing the data) that (most) young men tend to think women prefer more muscle than they themselves have. What is the value of the test…A paper company has about 50 paper mills distributed over 3 provinces. Each mill records specified factors that contribute to its profitability. The company has classified the mills as Profitable and Non- Profitable. They recorded paper weight produced as an indicator of profitability. That is, X₁ = PAPER (weight in 10000 kilograms) Y = PROF (1 = profitable and 0 = not profitable) Y Profitable 1 1 0 It was found that Paper 2 1.5 0.8 ît= exp(-2.94 + 0.098X₁) 1 + exp(-2.94 +0.098X₁) 1. Give the fitted logistic response function. 2. Give the fitted logit response function 3. Show that ft loge € (₁^²) = = -2.94 + 0.098X₁ 4. Give the odds to be used of this logistic regression for X₁ = 0.7. Explain your result. 5. What is the estimated probability that a mill be profitable if it produces 7 000 kilograms of paper? 7. Interpret the regression coefficients of ît= Also find the odds ratio for b₁. exp(-2.94 + 0.098X₁) 1 + exp(-2.94 +0.098X₁)
- A dermatologist compared a new treatment for athlete’s foot (the experimental condition) to the standard treatment (the control condition). He tracked down 30 people with athlete’s foot on both feet and, for each participant, randomly assigned one foot to receive the new treatment and the other foot to receive the standard treatment. After three weeks of treatment, he measured the percent- age of reduction in symptoms (the larger the number, the better the outcome). He found ME = 88, MC = 72, and sD = 8.65.To test the effectiveness of a new drug designed to relieve flu symptoms, 200 patients were randomly selected and divided into two equal groups. One group of 100 patients was given a pill containing the drug while the other group of 100 was given a placebo. What can we conclude about the effectiveness of the drug if 62 of those actually taking the drug felt a beneficial effect while 41 of the patients taking the placebo felt a beneficial effect? Use α = 0.05.A 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 125 patients from the city and estimates the following regression function: Y= 15.50 + 0..90B+1.15A. (0.55) (0 40) The test statistic of the study the student wants to conduct (Ho: B, = 0 vs. H, B, #0), keeping other variables constant is. (Round your answer to two decimal places.) At the 5% significance level, the student will ▼ the null hypothesis. Keeping BMIl constant, she now wants to 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…