A new vaccine against the coronavirus has been developed. The vaccine was tested on 10,000 volunteers and the study has shown that 65% of those tested do not get sick from the coronavirus. Unfortunately, the vaccine has side effects and in the study it was shown that the probability of getting side effects among those who did not get sick

A new vaccine against the coronavirus has been developed. The vaccine was tested on 10,000 volunteers and the study has shown that 65% of those tested do not get sick from the coronavirus. Unfortunately, the vaccine has side effects and in the study it was shown that the probability of getting side effects among those who did not get sick

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Until 2002, hormone replacement therapy (HRT), estrogen and/or progesterone, was commonly prescribed to post-menopausal women. This changed in 2002, when the results of a large clinical trial were published 7500 women were randomized to take HRT, 7100 were randomized to placebo. 170 HRT and 130 placebo women developed invasive breast cancer. Does HRT increase risk of breast cancer? Conduct hypothesis test. Hint: Use randomization distribution to answer the question.
Give two examples of Bernoulli trials other than those presented in the text.
There is a current chemotherapy drug available that is extremely successful in treating an aggressive form of breast cancer. This drug has as a serious side effect in that 20% of the recipients will subsequently go on to develop ALL, an often untreatable and fatal form of leukemia. The pharmaceutical company is developing a modified version of this drug and long term clinical trials are being conducted on 214 women afflicted with this aggressive form of breast cancer. The trials have indicated 31 subsequent cases of ALL. State and test the hypothesis that there is no difference in the proportion of ALL cases between the two chemotherapy drugs against the alternative that there is a difference. Set alpha equal to 0.02
A new vaccine against the coronavirus has been developed. The vaccine was tested on10,000 volunteers and the study has shown that 65% of those tested do not get sick from thecoronavirus. Unfortunately, the vaccine has side effects and in the study it was shown thatthe probability of getting side effects among those who did not get sick is 0.31, while theprobability of getting side effects among those who got sick from corona despite vaccinationis 0.15. (b) What is the probability that a randomly vaccinated person does not become ill with thecoronavirus and does not get side effects? (c) What is the probability that a randomly vaccinated person gets side effects? (d) What is the probability that a randomly vaccinated person who has not experienced sideeffects does not become ill with the coronavirus?
Teenagers who do not sleep well or long enough may have a higher risk of raised blood pressure, which could lead to cardiovascular disease later in life. The odds of raised blood pressure increase 3.5 times for those who have trouble falling asleep at night or who wake up too early and 2.5 times for those with sleeping periods of fewer than 6.5 hours. A health psychologist is interested in studying teenagers who have diastolic blood pressure scores in the top 20%. Diastolic blood pressure scores for teenagers follow a normal distribution with μ = 72 and σ = 10. Use the Distributions tool to help answer the questions that follow. The minimum z-score necessary to be in the top 20% of the diastolic blood pressure distribution is z =0.842 . Use this z-score to determine X, the corresponding diastolic blood pressure score. X = 80.42 This score, X, is the 80th percentile of diastolic blood pressure scores among teenagers. The percentile rank of this score is 80%…
A clinical trial is planned to compare an experimental medication designed to lower blood pressure to a placebo. Before starting the trial, a pilot study is conducted involving eight participants. The objective of the study is to assess how systolic blood pressure changes over time untreated. Systolic blood pressures are measured at baseline and again 4 weeks later Is there a statistically significant difference in blood pressures over time? Run the test at a 5% level of significance. Give each of the following to receive full credit: 1) the appropriate null and alternative hypotheses; 2) the appropriate test; 3) the decision rule; 4) the calculation of the test statistic; and 5) your conclusion including a comparison to alpha or the critical value. You MUST show all your work to receive full credit. Partial credit is available. Baseline 4 weeks 135 136 150 142 143 135 160 158 152 155 143 140 133 128 146 129
Bilirubin is a yellowish substance in your blood that forms after red blood cells break down and it travels through your liver, gallbladder, and digestive tract before being excreted. Elevated levels may indicate liver damage as your liver isn’t clearing bilirubin properly. A researcher is interested in estimating the mean Bilirubin level for a population of patients with liver disease along with its 90% confidence interval. The researcher collected data from a sample of 24 patients and found the average Bilirubin level is 86.08 with standard deviation 106. However, due to the skewness in the data, a natural logarithm of the data was performed to satisfy normality assumption required for calculating the confidence interval. The resulted 90% confidence interval for the mean Bilirubin level under the natural log transformation is (3.69,4.3). Which one of the following options best helps the researcher in making inference about the true population mean Bilirubin level? a. Based…
Based on past record of a pharmaceutical company, the cure rates for a standardmedication in treating a particular ailment is ten percent. After five years, thecompany has produced a new medication. The hired pharmacist in the companyclaims that the new medication produced by the company is effective in treating aparticular ailment compared to a standard medication. In a simple randomsample of two hundred subjects who took the new medication, it was found thatsixty subjects are uncured. Meanwhile, one hundred and eighty subjects arecompletely cured from three hundred subjects who took the standard medication.Given that the 97.8% confidence interval for the cure rates of the standardmedication is (0.5352, 0.6648). Can we conclude that the cure rates of thestandard medication do not change from the past record?
Trans-Generational Effects of Diet Can experiences of parents affect future children? New studies16 suggest that they can: Early life experiences of parents appear to cause permanent changes in sperm and eggs. In one study, some male rats were fed a high-fat diet with 43% of calories from fat (a typical American diet), while others were fed a normal healthy rat diet. Not surprisingly, the rats fed the high-fat diet were far more likely than the normal-diet rats to develop metabolic syndrome (characterized by such things as excess weight, excess fat, insulin resistance, and glucose intolerance.) What surprised the scientists was that the daughters of these rats were also far more likely to develop metabolic syndrome than the daughters of rats fed healthy diets. None of the daughters and none of the mothers ate a high-fat diet and the fathers did not have any contact with the daughters. The high-fat diet of the fathers appeared to cause negative effects for their daughters. What are the…
A clinical trial is planned to compare an experi- mental medication designed to lower blood pressure to a placebo. Before starting the trial, a pilot study is conducted involving 7 participants. The objective of the study is to assess how systolic blood pressure changes over time untreated. Systolic blood pres- sures are measured at baseline and again 4 weeks later. Is there a statistically significant difference in blood pressures over time? Run the test at a 5% level of significance. Baseline: 120 145 130 160 152 143 126 4 Weeks: 122 142 135 158 155 140 130
A study was made of 413 children who were hospitalized as a result of motor vehicle crashes. Among 290 children who were not using seat belts, 60 were injured severely. Among 123 children using seat belts, 16 were injured severely (based on data from "Morbidity Among Pediatric Motor Vehicle Crash Victims: The Effectiveness of Seat Belts," by Osberg and Di Scala, American Journal of Public Health, Vol. 82, No. 3). For this problem we want to know, is there sufficient sample evidence to conclude, at the 0.05 significance level, that the proportion of severe injuries is higher for children not wearing seat belts? Let pi be the proportion of severe injuries among all children not wearing seatbelts and who were involved in crashes. Let p2 be the proportion of severe injuries among all children wearing seatbelts and who were involved in crashes. Which is the proper expression of Ho? Pi = P2 O Pi P2 Which is the proper expression of H1? O pi P2 Calculate p1 to 4 decimal places: Calculate p,…