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

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.
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
Postpartum depression and anxiety (PPD), is a common medical condition affecting mothers and their families after the birth of a baby. The CDC estimated that 18% of women who have recently given birth suffer from PPD. However, this research only reflected self-reported cases. Therefore, one group dedicated to helping women and their families with PPD believes that the true percentage of women who suffer from PPD is much higher. The group conducts a simple random sample of 112 women who had given birth in the last year and discovers that 26 of them report having PPD. Based on this evidence, can the group claim that the true percentage of women who have PPD is greater than 18%? Use a 0.05 level of significance. Step 3 of 3 : Draw a conclusion and interpret the decision. 1. We reject the null hypothesis and conclude that there is sufficient evidence at a 0.05 level of significance that the true percentage of women who have PPD is greater than 18%. 2. We fail to reject the…
According to the CDC, as of MAY 2021, it is suspected that 2% of the US population currently have active coronavirus. According to Johns Hopkins, a particular type of COVID test (RT-PCR), has a false negative rate of 20%. That is, if a person has COVID, and takes this test, there is a 20% chance of testing negative. The false positive rate is about 5%. That means that about 5% of people who don't have COVID will nonetheless test positive. Consider the following two-way table for 10,000 randomly selected people who were tested for COVID using (RT-PCR). Positive test Negative test Total Has COVID A 40 200 No COVID 490 B 9800 Total 10000 1. fill in the missing values in the table. A • B • C • D 2. What is the probability of choosing someone who tested positive? 3. What is the probability of choosing someone who has COVID? 4. What is the probability of choosing someone who does not have COVID and tested positive? 5. What is the probability of choosing someone with COVID given that they…
An experiment was conducted to test if 2 new anti-anxiety medications will have an effect on number of anxiety symptoms. The researcher randomly assigned participants to one of the three experimental groups. Groups 1 and 2 took the 2 new medications while Group 3 took a placebo pill. The researcher was interested in determining whether there would be a difference in the number of anxiety symptoms among the three groups. Assume an alpha level of 0.05 and a two-tailed test. What statistical test should you use to evaluate the hypothesis above? one-way independent ANOVA Pearson Product-Moment Correlation simple linear regression multiple linear regression three-way independent ANOVA
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?
In 2018, a study was conducted that stated 22.6% of residents in Kern County live below the poverty line. Suppose you were hired to determine if that percentage has changed since the study was conducted. You randomly sample 200 residents from Kern County and find that 35 of them fall below the poverty line. Carry out the appropriate hypothesis test at the a = 0.05 level of significance to determine if the true proportion of Kern County residents that live below the poverty line is lower than what it was in 2018.
Can you please answer all of the questions in the picture please. Explain and show your work ON PICTURES PLEASE! IT'S EASY TO UNDERTAND.
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