Researchers at Boston’s Children’s Hospital and Harvard Medical School analyzed records of breast cancer screening and diagnostic evaluations (National Expenditure for False-Positive Mammograms and Breast Cancer Overdiagnoses Estimated at $4 Billion a Year,” Health Affairs [2015]: 576–583). Discussing the downsides of the screening process, the article states that the rate of false-positives is higher than previously thought, and that false-positives lead to unnecessary medical follow-up that can be costly.
Suppose that screening is used to decide between a null hypothesis of
H0: no cancer is present
and an alternative hypothesis of
Ha: cancer is present.
(Although these are not hypotheses about a population characteristic, this exercise illustrates the definitions of Type I and Type II errors.) (Hint: See Example 10.6.)
- a. Would a false-positive (thinking that cancer is present when in fact it is not) be a Type I error or a Type II error?
- b. Describe a Type I error in the context of this problem, and discuss the possible consequences of making a Type I error.
- c. Describe a Type II error in the context of this problem, and discuss the possible consequences of making a Type II error.
- d. Which type of error are the researchers concerned about when they say that false-positives lead to unnecessary medical follow-up? Explain why it would be reasonable to use a small significance level.
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Chapter 10 Solutions
Introduction To Statistics And Data Analysis
- In January 2007 Consumer, Reports published a study of bacterial contamination of chicken sold in the United States. They purchased 525 broiler chickens from various stores in 23 states and tested them for bacterial contamination. Lab tests indicated 83% of the chickens were contaminated with Campylobacter. How would you justify a claim by the USDA that the number of chickens tested was not large enough since 9 billion chickens are sold each year in the U.S.? What is the impact on the confidence interval estimate if a larger sample is used?arrow_forwardIn a study of 301 Hispanic women living in San Antonia, Texas, one variable of interest was the percentage of subjects with impaired fasting glucose (IFG). IFG refers to a metabolic stage intermediate between normal glucose homeostasis and diabetes. In the study, 24 women were classified in the IFG stage. The article cites population estimates for IFG among Hispanic women in Texas as 6.3%. Is there sufficient evidence to indicate the population of Hispanic women in San Antonio has a prevalence of IFG higher than 6.3%? Use 95% confidence level and the p -value method to form your conclusion. The computed z score was 1.193. Find the p-value.arrow_forwardIn a recent submission to a Joint Select Committee of Parliament, the National Consumers' League said “In reality, cow’s milk especially processed cow’s milk, has been linked to a variety of health problems, including: mucous production, haemoglobin loss, childhood diabetes, heart disease, arteriosclerosis, arthritis, kidney stones, mood swings, depression, irritability, allergies.” Researchers know this to be true, though the Committee rejected the submission. Suppose that 34% of the population has mood swings, allergies, irritability and depression (MAID) and is known to consume dairy products. Also, 80% of the populace consumes dairy products. Suppose a randomly chosen dairy products user is tested, what is the probability this person has MAID? Select one: a. 0.425 b. 0.460 c. 0.140 d. 0.272arrow_forward
- In a study of 301 Hispanic women living in San Antonia, Texas, one variable of interest was the percentage of subjects with impaired fasting glucose (IFG). IFG refers to a metabolic stage intermediate between normal glucose homeostasis and diabetes. In the study, 24 women were classified in the IFG stage. The article cites population estimates for IFG among Hispanic women in Texas as 6.3%. Is there sufficient evidence to indicate the population of Hispanic women in San Antonio has a prevalence of IFG higher than 6.3%? Use 95% confidence level and the p -value method to form your conclusion. Choose the correct null and alternative hypothesis.arrow_forwardIn a study of 301 Hispanic women living in San Antonia, Texas, one variable of interest was the percentage of subjects with impaired fasting glucose (IFG). IFG refers to a metabolic stage intermediate between normal glucose homeostasis and diabetes. In the study, 24 women were classified in the IFG stage. The article cites population estimates for IFG among Hispanic women in Texas as 6.3%. Is there sufficient evidence to indicate the population of Hispanic women in San Antonio has a prevalence of IFG higher than 6.3%? Use 95% confidence level and the p -value method to form your conclusion. Define x.arrow_forwardIn a study of 301 Hispanic women living in San Antonia, Texas, one variable of interest was the percentage of subjects with impaired fasting glucose (IFG). IFG refers to a metabolic stage intermediate between normal glucose homeostasis and diabetes. In the study, 24 women were classified in the IFG stage. The article cites population estimates for IFG among Hispanic women in Texas as 6.3%. Is there sufficient evidence to indicate the population of Hispanic women in San Antonio has a prevalence of IFG higher than 6.3%? Use 95% confidence level and the p -value method to form your conclusion. Answer the problem in a complete sentence.arrow_forward
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- The death rate per 100,000 for lung cancer is 7 among non-smokers and 71 among smokers. The death rate per 100,000 for coronary thrombosis is 422 among non-smokers and 599 among smokers. The prevalence of smoking in the population is 55%. The relative risk of dying for a smoker compared to a non-smoker is: [Refer to the chapter titled “Study Designs: Cohort Studies”] A. 9.1 for lung cancer and 0.30 for coronary thrombosis. B. 10.1 for lung cancer and 1.4 for coronary thrombosis. C. 10.1 for lung cancer and 8.4 for coronary thrombosis. D. 9.1 for lung cancer and 1.4 for coronary thrombosis. E. 12.4 for lung cancer and 1.7 for coronary thrombosis.arrow_forwardResearch indicates that there may be a relationship between caffeinated coffee consumption and risk of depression in women. Provided is data on the amount of caffeinated coffee consumed and whether the woman was diagnosed with clinical depression. Of interest is to see if there is evidence of an association between caffeinated coffee intake and clinical depression in women. What are the hypotheses? Caffeinated coffee Depression <1 cup/wk >=1 cup/day 2-3 cups/day 4+ cups/day Total Yes 670 1278 564 95 2607 No 11545 22573 11726 2288 48132 Total 12215 23851 12290 2383 50739 A. H0: H0 is not true and there is no association between caffeine intake and depression in women B. There is no association between caffeine intake and depression in women and H0 is not true C. Research indicates that there may be a relationship between caffeinated coffee consumption and risk of depression in women D. H0: There is an association between caffeine intake and…arrow_forwardNCI Cancer Bulletin, December 2, 2008 Volume 5 / Number 24 Title of the article: After Menopause, Weight Affects Breast Cancer Rates More than Mammography Use Women who are overweight or obese after menopause face an increased risk of breast cancer, but a large prospective cohort study indicates that the frequency of mammography use and screening accuracy are not the primary explanations for higher rates of breast cancer in these women. The same is true of large, invasive breast cancer tumors and advanced stage disease; risk increases with weight, but higher rates are not explained by the frequency or accuracy of screening mammography before breast cancer was diagnosed. The study appears in the December 3 Journal of the National Cancer Institute. Dr. Karla Kerlikowske of the San Francisco Veterans Affairs Medical Center and colleagues gathered data on 287,115 postmenopausal women who were registered in the Breast Cancer Surveillance Consortium database. Reflecting a trend in the…arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill