8. Two randomized, double-blind studies (Study X and Study Y) are conducted to assess the efficacy of a new chemotherapeutic agent. For each study, patients are randomized to receive either placebo or the new experimental chemotherapy, all subjects are then followed for a mean of 5 years. Follow-up rates are 92% in Study X and 91% in Study Y. Results show 84 Study X Study Y ETITI Lower socioeconomic Average age (years) Caucasian (%) Experiment 53 Control Experiment 52 50 84 89 Current smoker (%) 15 14 14 Control 52 86 13 25 28 30 27 Local cancer (%) Heart disease (%) Diabetes (%) 75 77 72 10 12 10 74 10 15 7 10 9 status (%) The relative risk of dying of cancer is 0.7 in Study X (95% confidence interval of 0.2 to 2.4) and 0.6 in Study Y (95% confidence interval of 0.5 to 0.7). Which of the following best accounts for this difference in confidence intervals? A) Bias B) Difference in follow-up rates C) Difference in number of patients D) Different population E) Randomization error

8. Two randomized, double-blind studies (Study X and Study Y) are conducted to assess the efficacy of a new chemotherapeutic agent. For each study, patients are randomized to receive either placebo or the new experimental chemotherapy, all subjects are then followed for a mean of 5 years. Follow-up rates are 92% in Study X and 91% in Study Y. Results show 84 Study X Study Y ETITI Lower socioeconomic Average age (years) Caucasian (%) Experiment 53 Control Experiment 52 50 84 89 Current smoker (%) 15 14 14 Control 52 86 13 25 28 30 27 Local cancer (%) Heart disease (%) Diabetes (%) 75 77 72 10 12 10 74 10 15 7 10 9 status (%) The relative risk of dying of cancer is 0.7 in Study X (95% confidence interval of 0.2 to 2.4) and 0.6 in Study Y (95% confidence interval of 0.5 to 0.7). Which of the following best accounts for this difference in confidence intervals? A) Bias B) Difference in follow-up rates C) Difference in number of patients D) Different population E) Randomization error

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter9: Sequences, Probability And Counting Theory

Section9.7: Probability

Problem 3SE: What is an experiment?

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What is an experiment?
A researcher is comparing the occurrence of nausea as a side-effect in two brands of medication: Brand A and Brand B. For a random sample of 150 Brand A users, 66 experienced nausea as a side-effect. For a random sample of 200 Brand B users, 118 experienced nausea as a side-effect. Can the researcher conclude that the proportion of all Brand A users who experience nausea as a side-effect is different from the proportion of all Brand B users who experience nausea as a side-effect. For the hypothesis testing scenario above, the researcher concludes that the two proportions are different at the 0.01 significance level. Compute the 99% confidence interval to estimate the difference.
A researcher is studying two types of medication that both treat hives. 23 out of the random sample of 334 adults given medication A still had hives 30 minutes after taking the medication. 18 out of another random sample of 346 adults given medication B still had hives 30 minutes after taking the medication. Test to see if the proportion of people who still had hives after medicine A is different than the proportion of people who still had hives after medicine B. Use a 0.01 level of significance.
3.) In a randomized experiment, double-blind clinical trials of Prevnar, infants were randomly divided into twogroups. Subjects in group 1 received Prevnar, while subjects in group 2 received a control vaccine. After the seconddose, 137 of 452 subjects who received Prevnar experienced drowsiness as a side effect. After the second dose, 31of 99 subjects who the control vaccine experienced drowsiness as a side effect. Does the evidence suggest that alower proportion of subjects who took Prevnar experienced drowsiness as a side effect than subjects who had thecontrol vaccine at the ? = 0.01 level of significance?a.) Verify that the requirements for inference about two population proportions is satisfied.b.) What is the Null and Alternative Hypotheses? What test will you be using?c.) What is the level of significance and the ?-value?
4. 15 healthy adult subjects were asked to walk on a treadmill while connected to monitors. One of two kinds of disturbances was applied during the walk, and the number of steps until adaptation was recorded. Each subject experienced both kinds of disturbance, in random order and the researchers computed the difference between the two disturbances and were interested if the mean effect of the first disturbance was greater than the mean effect of the second. c. Based on the P-value, what conclusion can be drawn at a 5% significancelevel?
A smartphone manufacturer is so certain of its quality control that it offers a complete replacement warranty if the smartphone fails within 3 years. Based upon compiled data, the company notes that there is a 2 percent chance that its smartphone will fail during the first year, a 10 percent chance that a smartphone that survives the first year fails during the second year, and a 20 percent chance that a smartphone that survives the first two years fails during the third year. The warranty does not cover replacement smartphones after the third year. (a) Formulate the evolution of the status of the smartphone as a Markov Chain whose states include two abosrbing states that involve needing to honor the warranty or having the smartphone survive the warranty period. Construct the transition probability matrix and draw the transition probability diagram. (b) Determine the probability that: (a) the manufacturer will have to honor the warranty and (b) the manufacturer will not…
Suppose that we are counting successes in a Bernoulli process with success rate .4. In 200 independent trials, what is the variance in the number of successes?
Suppose that a large controlled experiment tests whether caffeine improves reaction times. A very large number of randomly selected participants are randomly given identical-seeming pills with varying doses of caffeine (including none) and then given tests of reaction times under the same conditions. The experiment finds a strong negative correlation between caffeine dose and reaction time. (Note that lower reaction times are better.) Select the correct answer below: 1. There is evidence that caffeine causes lower (better) reaction times. 2. People with lower (better) reaction times generally choose to consume more caffeine. 3. Lower reaction times are associated with higher caffeine doses, but this study provides no evidence that caffeine causes lower reaction times. 4. There is no relationship between reaction time and caffeine.
Suppose, when conducting a 2-way ANOVA, you find significant main effects for both of your factors of interest (i.e. gender and educational attainment, categorized as high school graduate or less vs. more than a high school education), but no significant interaction between the 2 factors. Which of the following statements, if any, are reasonable conclusions? Question 22 options: A) Since there is no significant interaction between gender and educational attainment, we can conclude that the outcome does not differ between groups. B) Since there is a significant main effect for gender, then the outcome must be significantly different between males and females. C) Since there is a significant main effect for educational attainment, then the outcome must be significantly different between the 2 educational attainment groups. D) All of the above are reasonable conclusions. E) Answers B and C are reasonable…
A consumer products testing group is evaluating two competing brands of tires, Brand 1 and Brand 2. Though the two brands have been comparable in the past, some technological advances were recently made in the Brand 1 manufacturing process, and the consumer group is testing to see if Brand 1 will outperform Brand 2. Tread wear can vary considerably depending on the type of car, and the group is trying to eliminate this effect by installing the two brands on the same random sample of 8 cars. In particular, each car has one tire of each brand on its front wheels, with half of the cars chosen at random to have Brand 1 on the left front wheel, and the rest to have Brand 2 there. After all of the cars are driven over the standard test course for 20,000 miles, the amount of tread wear (in inches) is recorded, as shown in Table 1. Car Brand 1 Brand 2 Difference(Brand 1 - Brand 2) 1 0.275 0.425 -0.150 2 0.319 0.400 -0.081 3 0.317 0.358 -0.041 4 0.250 0.247 0.003 5…
In an ANOVA problem involving six treatments and 14 observations per treatment, SSE = 234. The MSE for this scenario is _______.