Grouping together similar experimental units and then randomly assigning the experimental units within each group to a treatment is called
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- A pharmaceutical company tested the impact of four cholesterol-reducing medications (denoted A, B, C and D) on people at high risk of heart attack. For this clinical trial 20 volunteers with LDL (bad) cholesterol levels of 140 mg/dl were randomly assigned to one of the four medications. The subjects were instructed to take one tablet per day for a period of three months after which their LDL levels were again measured. Below are the amounts (in mg/dl) by which the LDL levels decreased after the three month trial. Medication A Medication B Medication C Medication D 29 31 30 31 30.5 30 32 31.5 30.5 32 31.75 35 31 29.75 27 33 29 31.5 33 29 (d) What assumptions are needed to make this test valid? (e) If a key assumption in (d) is not satisfied, test if the data provide sufficient ev- idence to indicate that at least one of the medications produces a mean reduc- tion in LDL cholesterol that is different from any of the other medications using a non-parametric method (show all working and…A professor of women's studies is interested in determining if stress affects the menstrual cycle. Ten women are randomly sampled for an experiment and randomly divided into two groups. One of the groups is subjected to high stress for two months while the other lives in a relatively stress-free environment. The professor measures the menstrual cycle (in days) of each woman during the second month. The following data are obtained. High stress 20 23 18 19 22 Relatively stress free 26 31 25 26 30 Assume you are evaluating H0 using the t test. The df for determining tcrit are _________.The data in table is from a randomized block design represent blood pressure measurements from an experiment involving 4 age groups, each with 3 persons. The 3 persons within each age group were randomly assigned to drugs, A, B and C with one person per drug. This was done to keep the drug assignments balanced within age groups. Comparing the three drugs in manner that provides balance for or control for possible age effects. Consider the data given in table below and compute; a. Mean Square Due to Treatments (MSTR) b. Mean Square Due to Blocks (MSBL) Mean Square Due to Error (MSE) C. d. F-test Treatments Age Groups (Blocks) A B 1 70 72 2 76 84 3 82 86 4 90 92 Total 318 334 C Total Blocks 80 222 82 242 84 252 88 270 334 986
- A coffee company wants to determine how long caffeine lasts throughout the day when individuals have a cup of one of their 3 types of coffee at 9am. They will then measure the levels of caffeine in these individuals’ systems at 10am, 12am, 2pm, 4pm, 6pm and 8pm. They want to have at least 20 observations per group. How many separate/distinct groups of participants are needed if they want to conduct this experiment using a mixed-measures ANOVA? options: a. Not enough information to determine b. 18 c. 6 d. 20 e. 3Researchers investigate how the presence of cell phones influence the quality of human interaction. Subjects are randomly selected from a population and divided into an experimental group that is asked to leave their phones in the front of the room and a control group that are not asked to leave their cell phones at the front of the room. Subjects are left alone for 10 minutes and then asked to take a survey designed to measure quality of interactions they had with others in the experiment. What statistical test is appropriate?Two professors at a local college developed a new teaching curriculum designed to increase students' grades in math classes. In a typical developmental math course, 55% of the students complete the course with a letter grade of A, B, or c. In the experimental course, of the 19 students enrolled, 13 completed the course with a letter grade of A, B, or C. Is the experimental course effective at the a = 0.025 level of significance? Complete parts (a) through (g). (Round to one decimal place as needed.) (c) Explain why this is a binomial experiment. There is a number of trials with The trials independent and the probability of success is fixed at for each trial. (Type an integer or a decimal. Do not round.)
- The General Social Survey (GSS) collects data on demographics, eduction and work, among many other characteristics of US residents. Suppose we want to estimate the difference between the average number of hours worked by all Americans with a college degree and those without a college degree. Is there sufficient evidence that there is a significant difference between the average number of hours worked by those Americans with a college degree vs. those Americans without a college degree? Use the following output: Welch Two Sample t-testdata: yes and not = 3.1181, df = 1098.5, p-value = 0.001867alternative hypothesis: true difference in means is not equal to 095 percent confidence interval: 1.011652 4.445822sample estimates:mean of x mean of y 42.81574 40.08701 Using the provided output, find the 95% confidence interval for the difference of the average amount of hours worked for those that have a college degree vs. those that do not have a college degree (ie: for the difference of two…Acne is a common skin disease that affects most adolescents and can continue into adulthood. A study compared the effectiveness of three acne treatments and a placebo, all in gel form, applied twice daily for 12 weeks. The study's 517 teenage volunteers were randomly assigned to one of the four treatments. Success was assessed as clear or almost clear skin at the end of the 12 week period. The results of the study can be seen in the table below. Using the appropriate statistical test, determine if there is significant evidence that the four treatments perform differently. If so, how do they compare.A researcher wants to test the effectiveness of a new drug to treat asthma. One hundred patients with chronic, stable asthma were randomly assigned to one of three groups to receive a placebo (0mg), 1mg of drug, or 5 mg of drug. After treatment, a doctor tested the patient’s forced expiratory volume for 1 second (FEV1). Which statistical test would be best to determine if there is a significant difference between groups? one-sample t-test dependent samples t-test independent samples t-test ANOVA
- An investigation is performed to evaluate two new experimental treatments for allergies. 18 subjects who suffer from allergies are enrolled in the study and randomly assigned to one of three treatments: Control Group, Experimental Treatment 1, or Experimental Treatment 2. Each subject is instructed to take the assigned treatment, and symptoms of allergies are recorded on a scale of 1 to 20, with higher scores indicating worse symptoms. The data is summarized in the table below: SBP Std. Deviation Group Mean Control Treatment 6. 16.17 2.483 Experimental Treatment 1 6. 11.33 1.966 Experimental Treatment 6. 3.83 1.472 Total 18 10.44 5.554 Use this data to complete an ANOVA table to test for a significant difference in the means of each of the groups. Round all answers to the third decimal point.How long it takes paint to dry can have an impact on the production capacity of a business. An auto body & paint business invested in a paint-drying robot to speed up its process. An interesting question is, "Do all paint-drying robots have the same drying time?" To test this, suppose we sample five drying times for each of different brands of paint-drying robots. The time in minutes until the paint was dry enough for a second coat to be applied was recorded. Suppose the following data were obtained. Robot 4 Robot 1 128 138 134 125 135 Robot 2 143 134 142 147 | Ho: M₁ = 1₂ = 13 = 14 H₂: M₁ # M₂ # Hz # H4 124 4ܐ = 3ܬܐ = 2ܬܐ = 1ܐ :Ha Robot 3 132 142 | Ho: M₁ # M₂ # M3 # H4 H₂: M₁ = 1₂ = 13 = 14 138 135 128 ⒸH₁: M₁ = H₂ = 143 = 14 H: Not all the population means are equal. 151 142 At the α = 0.05 level of significance, test to see whether the mean drying time is the same for each type of robot. State the null and alternative hypotheses. O Ho: Not all the population means are equal. 136…In a certain study, the effect on oat yield was compared for the Pallinup, Overberg and Magnifico varieties of oats and four different concentrations of manure (0, 0.2, 0.4 and 0.6 tonnes per acre). Identify the experimental units, response variable, factor(s), levels of each factor and treatments.
