Question 6 Suppose that among 10,000 women with negative mammograms, 20 will bediagnosed with breast cancer within 2 years, whereas 1 woman in 10 with positivemammograms will be diagnosed with breast cancer within 2 years. Assume that 7% ofthe general population of women will have a positive mammogram. Is the fact that arandomly selected woman has positive mammogram is independent of the fact that thewoman will be diagnosed with breast cancer within 2 years? What is the probability ofdeveloping breast cancer over the next 2 years among women in the general population?

From the given information, among 10,000 women with negative mammograms, 20 will be diagnosed with…

Answered: Question 6 Suppose that among 10,000…

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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A random selection of volunteers at a research institute has been exposed to a weak flu virus. After the volunteers began to have flu symptoms, 20 of them were given multivitamin tablets daily that contained 1 gram of vitamin C and 3 grams of various other vitamins and minerals. The remaining 20 volunteers were given tablets containing 4 grams of vitamin C only. For each individual, the length of time taken to recover from the flu was recorded. At the end of the experiment the following data were obtained. Treated with multivitamin Treated with vitamin C Days to recover from flu 7.2, 5.3, 4.9, 4.4, 2.0, 4.0, 5.9, 4.9, 5.2, 7.7, 4.2, 7.3, 5.0, 7.3, 7.5, 3.0, 6.4, 6.5, 7.1, 4.6 2.9, 2.7, 5.4, 3.9, 4.7, 4.0, 5.9, 2.9, 6.8, 5.8, 7.0, 4.0, 1.6, 6.0, 3.7, 3.9, 4.5, 0.4, 6.4, 0.9 Send data to Excel Send data to calculator Lower limit: Upper limit: Suppose that it is known that the population standard deviation of recovery time from the flu is 1.8 days when treated with multivitamins and that…
Help me please!! A report from a certain NGO stated that on average a woman visits her physician 5.8 times a year. A researcher randomly selects 20 women and obtained these data. 3 2 1 3 7 2 9 4 6 6 8 0 5 6 4 2 1 3 4 1 At a = 0.05 can it be concluded that the average is still 5.8 visits per year?
A pharmaceutical company proposed a vaccine that would combat paralytic polio. Two independent random samples were collected from the population. One random sample of 201,229 was given the placebo, and among them 100,910 contracted paralytic polio. The other random sample of 200,745 was given the vaccine, and among them 50,033 people ended up contracting paralytic polio. Let the true proportion of cases of paralytic polio given placebo be p1p1 and the true proportion of cases of paralytic polio given vaccine be p2. Calculate the upper bound of a 95% confidence interval for p1−p2. Round your answer to three decimal places.
The null hypothesis: H. :|| The alternative hypothesis: H :0 1 The type of test statistic: (Choose one) v The value of the test statistic: (Round to at least three decimal places.) The p-value: (Round to at least three decimal places.) Can we reject the researchers' claim that the mean recovery time when treated with multivitamin is less than or equal to the mean recovery time when treated with vitamin C only? Yes No
2. When she was 9 years old, Emily Rosa did a science fair experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left hand, then she asked the therapists to identify the selected hand by placing their hand just under Emily's hand without seeing it and touching it. Among the 280 trials, therapists were correct 123 times. Do the data provide sufficient evidence to indicate that touch therapists are effective? Test at the 1% level with both the critical value and p-value methods.
Each year, more than 2 million people in the United States become infected with bacteria that are resistant to antibiotics. In particular, the Centers of Disease Control and Prevention have launched studies of drug-resistant gonorrhea.† Suppose that, of 189 cases tested in a certain state, 12 were found to be drug-resistant. Suppose also that, of 429 cases tested in another state, 8 were found to be drug-resistant. Do these data suggest a statistically significant difference between the proportions of drug-resistant cases in the two states? Use a 0.02 level of significance. (Let p1 = the population proportion of drug-resistant cases in the first state, and let p2 = the population proportion of drug resistant cases in the second state.) State the null and alternative hypotheses. (Enter != for ≠ as needed.) H0: ______ Ha: ______ Find the value of the test statistic. (Round your answer to two decimal places.) = What is the p-value? (Round your answer to four decimal places.) p-value =…
Is the national crime rate really going down? Some sociologists say yes! They say that the reason for the decline in crime rates in the 1980s and 1990s is demographics. It seems that the population is aging, and older people commit fewer crimes. According to the FBI and the Justice Department, 70% of all arrests are of males aged 15 to 34 years†. Suppose you are a sociologist in Rock Springs, Wyoming, and a random sample of police files showed that of 33arrests last month, 25were of males aged 15 to 34 years. Use a 1%level of significance to test the claim that the population proportion of such arrests in Rock Springs is different from 70%. a. What is the level of significance? answer .01 b.State the null and alternate hypotheses. Which one? Its the third. H0: p< 0 .7; H1: p= 0.7 H0: p≠0.7; H1: p= 0.7 H0: p= 0.7; H1: p≠0.7 H0: p= 0 .7; H1: p< 0.7 H0: p= 0.7; H1: p> 0.7 c. What sampling distribution will you use? Its the last one. The Student's t, since np> 5 and…
A researcher is creating a new treatment protocol for Myelodysplastic Syndrome (MDS), a form of preleukemia. Following the old treatment protocol, 28% of patients with MDS will develop leukemia within 5 years of MDS diagnosis. He believes his new treatment protocol will lead to fewer MDS patients developing leukemia. He takes a random sample of 100 individuals on his new treatment protocol. Of these 100 individuals, 20 develop leukemia within 5 years of MDS diagnosis. In questions 8-9, create a 98% confidence interval for the true proportion of all MDS patients on this new treatment who will develop leukemia within 5 years of MDS diagnosis. What is the confidence interval? Do not round your answer. What is the interpretation of your confidence interval?
An experiment to test the effectiveness of regular treatments with fluoride varnish to reduce tooth decay involved 36 volunteers who had half of their teeth (the right side or left side, determined by a coin flip) painted with a fluoride varnish every six month for 5 years. At the end of the treatments, the number of new cavities during the treatment period was compared on treatment (fluoride varnish) side versus the control (no fluoride varnish) side. The appropriate statistical test for analyzing the results of this experiment is O Paired t test for a mean difference O One sample z test for a population mean O Two sample t test for a difference in means O One sample z test for a population proportion O Two sample z test for a difference in proportions
A research team is interested in investigating the effectiveness of a new medication intended to reduce resting heart rate (beats per minute, BPM) in overweight patients. In order to test the medication, the researcher organizes a clinical trial with participants randomly assigned to receive either the new medication or a placebo. Suppose the following table represents the heart rates for a SRS from both groups. Data for the placebo group are {71, 71, 68, 67, 68, 69, 70, 70, 69, 72, 73} Data for the treatment group are {67, 66, 64, 64, 65, 64, 59, 63, 71, 64} Sample standard deviation for the placebo group is: 1.834 Sample standard deviation for the treatment group is: 3.057 What is the confidence interval? (alpha=0.05) Group of answer choices (0.969492 to 9.266508) (2.31312 to 7.92288) (2.598132 to 7.637868) (-1.796934 to 12.032934)
A random selection of volunteers at a research institute has been exposed to a weak flu virus. After the volunteers began to have flu symptoms, 20 of them were given multivitamin tablets daily that contained 1 gram of vitamin C and 3 grams of various other vitamins and minerals. The remaining 20 volunteers were given tablets containing 4 grams of vitamin C only. For each individual, the length of time taken to recover from the flu was recorded. At the end of the experiment the following data were obtained. Treated with multivitamin Treated with vitamin C Days to recover from flu 3.2, 7.3, 8.4, 6.1, 2.5, 6.7, 6.3, 3.7, 7.0, 7.7, 9.1, 9.9, 9.0, 2.6, 2.0, 5.1, 5.7, 2.5, 2.9, 4.5 2.7, 5.3, 3.7, 5.5, 4.5, 3.8, 7.6, 5.3, 3.6, 5.2, 2.3, 4.7, 3.6, 5.2, 2.3, 7.1, 3.3, 6.1, 7.9, 4.2 Send data to calculator. Send data to Excel Suppose that it is known that the population standard deviation of recovery time from the flu is 1.8 days when treated with multivitamins and that the population standard…
Fifteen years ago, a complete survey of all undergraduate students at a large University indicated that the average student smoked 7.7 cigarettes per day. Th director of the student health center wishes to determine whether the incidence of cigarette smoking at his University has lessened over the fifteen year period. He obtains the following results (in cigarettes smoked per day) from a random sample of 9 students. 6.1, 9.2, 5, 6.3, 4.8, 3.2, 7.6, 8.1, 9. Test the null hypothesis at the .05 level significane.

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