A clinical trial is being conducted in order to determine the efficacy of a new drug that will be used to treat Crohn’s disease. The efficacy of the medication will not only be determined by the physical improvement of symptoms but will also be determined by using a blood test to examine the concentration C-reactive protein (an inflammatory marker) in an individual’s blood. If the researcher wants a margin of error for the level of C-reactive protein to be less than or equal to 2.9 mg/dL and the standard deviation for C-reactive protein concentrations among Crohn’s disease patients was previously documented at 10.1 mg/dL, how many patients should be recruited for each group of individuals in the study, assuming a 95% confidence interval will be used to quantify the mean differences between the control group and the treatment group?

A new analytical method to detect pollutants in water is being tested. This new method of chemical analysis is important because, if adopted, it could be used to detect three different contaminates - organic pollutants, volatile solvents, and chlorinated compounds - instead of having to use a single test for each pollutant. The makers of the test claim that it can detect high levels of organic pollutants with 99.6% accuracy, volatile solvents with 99.91% accuracy, and chlorinated compounds with 89.4% accuracy. If a pollutant is not present, the test does not signal. Samples are prepared for the calibration of the test and 60% of them are contaminated with organic pollutants, 27% with volatile solvents, and 13% with traces of chlorinated compounds. A test sample is selected randomly. (a) What is the probability that the test will signal? (b) If the test signals, what is the probability that the chlorinated compounds are present? Carry out all calculations exactly, then round the final…

A sleep researcher is assessing the impact of melatonin supplements on time to fall asleep for individuals with insomnia. She recruited 30 participants with insomnia and assigned 14 of them to take melatonin before sleeping. The researcher then recorded time to fall asleep (in minutes) for each participant. The researcher's hypothesis was that participants in the melatonin group would fall asleep faster than participants in the control group. The data collected are displayed below together with some descriptive statistics. Melatonin- 72, 59, 76, 64, 40, 51, 39, 69, 69, 78, 66, 100, 43, 45,59,64,51 M = 62.21 SD = 17.33 Control- 52, 80, 113, 111, 103, 96, 64, 56, 112, 102, 100, 102, 101, 58, 117, 101,80,111,96,56,102 M = 91.75 SD = 22.16 a) Does the researcher have enough evidence to reject the null hypothesis at an alpha level of .01? Follow the steps involved in hypothesis testing and make a decision regarding the null hypothesis based on the comparison between the critical value and…

A clinical trial is being conducted in order to determine the efficacy of a new drug that will be used to treat Crohn’s disease. The efficacy of the medication will not only be determined by the physical improvement of symptoms but will also be determined by using a blood test to examine the concentration C-reactive protein (an inflammatory marker) in an individual’s blood. If the researcher wants a margin of error for the level of C-reactive protein to be less than or equal to 2.9 mg/dL and the standard deviation for C-reactive protein concentrations among Crohn’s disease patients was previously documented at 10.1 mg/dL, how many patients should be recruited for each group of individuals in the study, assuming a 95% confidence interval will be used to quantify the mean differences between the control group and the treatment group? Group of answer choices nfor the treatment group = 12 and n for the control group = 12 nfor the treatment group = 14 and n for the control group = 14…

A researcher is studying two types of medication that both treat hives. 18 out of the random sample of 201 adults given medication A still had hives 30 minutes after taking the medication. 22 out of another random sample of 212 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 less than the proportion of people who still had hives after medicine B. Use a 0.05 level of significance. The correct hypotheses are: O Ho: PA HA PA Ho: PA HA PA O Ho: PA HA PA = PB PB(claim) The p-value is: PB PB(claim) PB PB(claim) Since the level of significance is 0.05 the critical value is -1.645 (round to 3 places) The test statistic is: (round to 3 places)

Your cognitive capacity is significantly reduced when your smartphone is within reach, even if it’s off.  A professor conducted experiments with nearly 600 smartphone users in an attempt to measure how well people can complete tasks when they have their smartphones nearby even when they’re not using them. In one experiment, the researchers asked study participants to sit at a computer and perform a task that required full concentration in order to succeed. The tests were geared to measure participants’ available cognitive capacity – that is, the brain’s ability to hold and process data at any given time. Before beginning, participants were randomly instructed to place their smartphones either on the desk face down (group 1; 200 participants), in their pockets (group 2; 200 participants), or in another room (group 3; 200 participants). All participants were instructed to turn their phones to silent. The researchers found that participants with their phones in another room significantly…

An antidepressant has historically been known to relieve depression for 65% of patients who use the drug. The drug's formula was changed recently to include smaller dose of its main, active ingredient. Due to this change, a medical researcher suspects that among all people with depression who use the new version of the drug, the proportion, p, of people who find relief is lower than 65%. A random sample of 240 patients who use the new version is selected by the researcher, and 149 of them find relief from depression. Based on these data, can we support the researcher's claim at the 0.05 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the alternative hypothesis H,. Ho :0 H¡ :0 (b) Determine the type of test statistic to use. (Choose one) ▼ OSO (c) Find the…

A researcher is studying two types of medication that both treat hives. 18 out of the random sample of 201 adults given medication A still had hives 30 minutes after taking the medication. 22 out of another random sample of 212 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 less than the proportion of people who still had hives after medicine B. Use a 0.05 level of significance. The correct hypotheses are: O Ho: PA HA PA Ho: PA HA PA O Ho: PA HA PA = PB PB(claim) The p-value is: PB PB(claim) PB PB(claim) Since the level of significance is 0.05 the critical value is -1.645 (round to 3 places) The test statistic is: (round to 3 places)

Recent studies have shown that adult men suffer from high blood pressure at a lesser rate than do adult women. To test that claim, a research randomly selected 200 of each gender and tested their blood pressure. The results revealed that 49 of the men and 62 of the women suffered from high blood pressure. Can you conclude that the proportion of men with high blood pressure is less than the proportion of women? Use α = 0.05.

A patient is classified as having gestational diabetes if their average glucose level is above 140 milligrams per deciliter (mg/dl) one hour after a sugary drink is ingested. Rebecca's doctor is concerned that she may suffer from gestational diabetes. There is variation both in the actual glucose level and in the blood test that measures the level. Rebecca's measured glucose level one hour after ingesting the sugary drink varies according to the Normal distribution with μ=140+5 mg/dl and σ=5+1 mg/dl. Using the Central Limit Theorem, determine the probability of Rebecca being diagnosed with gestational diabetes if her glucose level is measured: Once? n=5+2 times n=5+4 times Comment on the relationship between the probabilities observed in (a), (b), and (c). Explain, using concepts from lecture why this occurs and what it means in context.