Intro Stats, Books a la Carte Edition (5th Edition)
5th Edition
ISBN: 9780134210285
Author: Richard D. De Veaux, Paul Velleman, David E. Bock
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 16, Problem 28E
Alzheimer’s Testing for Alzheimer’s disease can be a long and expensive process, consisting of lengthy tests and medical diagnosis. A group of researchers (Solomon et al., 1998) devised a 7-minute test to serve as a quick screen for the disease for use in the general population of senior citizens. A patient who tested positive would then go through the more expensive battery of tests and medical diagnosis. The authors reported a false-positive rate of 4% and a false-negative rate of 8%.
- a) Put this in the context of a hypothesis test. What are the null and alternative hypotheses?
- b) What would a Type I error mean?
- c) What would a Type II error mean?
- d) Which is worse here, a Type I or Type II error? Explain.
- e) What is the power of this test?
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
A pharmaceutical company is testing a new drug for a rare disease. In a clinical trial, 1000 patients
with the disease were randomly assigned to receive either the new drug or a placebo. After one
year, it was found that 60% of the patients who received the new drug experienced improvement,
compared to only 40% of those who received the placebo. Is the difference in improvement rates
statistically significant? Provide your rationale.
In an observational study it was found that people who had received the flu shot this year had better blood pressure readings, on average, than people who did not. Can it be claimed that the flu shot is the cause of the lower overall blood pressure? Why or why not?
A health officer is trying to study the malaria situation of Zambia. From the records of seasonal blood survey (SBS) results he came to understand that the proportion of people having malaria in Zambia was 3.8% in 2015. The size of the sample considered was 15,000. He also realized that during the year that followed (2016), blood samples were taken from 10,000 randomly selected persons. The result of the 2016 seasonal blood survey showed that 200 persons were positive for malaria. Help the Health officer in testing the hypothesis that the malaria situation of 2016 did not show any significant difference from that of 2015 (take the 5% level of significance).
Chapter 16 Solutions
Intro Stats, Books a la Carte Edition (5th Edition)
Ch. 16.2 - An experiment to test the fairness of a roulette...Ch. 16.2 - Prob. 2JCCh. 16.2 - Prob. 3JCCh. 16.3 - Prob. 4JCCh. 16.3 - Prob. 5JCCh. 16.3 - Prob. 6JCCh. 16.3 - Prob. 7JCCh. 16.4 - Remember the bank thats sending out DVDs to try to...Ch. 16.4 - Prob. 9JCCh. 16.4 - For the bank, which situation has higher power: a...
Ch. 16 - True or false Which of the following are true? If...Ch. 16 - False or true Which of the following are true? If...Ch. 16 - P-values Which of the following are true? If...Ch. 16 - Prob. 4ECh. 16 - Prob. 5ECh. 16 - Prob. 6ECh. 16 - Prob. 7ECh. 16 - More critical values For each of the following...Ch. 16 - Prob. 9ECh. 16 - Significant again? A new reading program may...Ch. 16 - SECTION 16.4 11. Errors For each of the following...Ch. 16 - More errors For each of the following situations,...Ch. 16 - CHAPTER EXERCISES 13. P-value A medical researcher...Ch. 16 - Prob. 14ECh. 16 - Alpha A researcher developing scanners to search...Ch. 16 - Prob. 16ECh. 16 - Prob. 17ECh. 16 - Is the Euro fair? Soon after the Euro was...Ch. 16 - Prob. 19ECh. 16 - Prob. 20ECh. 16 - Prob. 21ECh. 16 - Prob. 22ECh. 16 - Prob. 23ECh. 16 - Prob. 24ECh. 16 - Prob. 25ECh. 16 - Prob. 26ECh. 16 - Prob. 27ECh. 16 - Alzheimers Testing for Alzheimers disease can be a...Ch. 16 - Prob. 29ECh. 16 - Quality control Production managers on an assembly...Ch. 16 - Cars, again As in Exercise 29, state regulators...Ch. 16 - Prob. 32ECh. 16 - Equal opportunity? A company is sued for job...Ch. 16 - Stop signs Highway safety engineers test new road...Ch. 16 - Prob. 35ECh. 16 - Ads A company is willing to renew its advertising...Ch. 16 - Prob. 37ECh. 16 - Prob. 38ECh. 16 - Prob. 39ECh. 16 - Catheters During an angiogram, heart problems can...Ch. 16 - Prob. 41ECh. 16 - Prob. 42ECh. 16 - Prob. 43ECh. 16 - Faulty or not? You are in charge of shipping...Ch. 16 - Prob. 45ECh. 16 - Prob. 46ECh. 16 - Prob. 47ECh. 16 - Prob. 48E
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- You are concerned that nausea may be a side effect of Tamiflu, but you cannot just give Tamiflu to patients with the flu and say that nausea is a side effect if people become nauseous. This is because nausea is common for people who have the flu. From past studies you know that about 31% of people who get the flu experience nausea. You collected data on 2211 patients who were taking Tamiflu to relieve symtoms of the flu, and found that 741 experienced nausea. Use a 0.01 significance level to test the claim that the percentage of people who take Tamiflu for the relief of flu symtoms and experience nausea is greater than 31%.arrow_forwardA recent study on the effects of Tamiflu looked into whether the antiviral medication can reduce the duration of the flu or not. To test this, researchers selected sample of 42 individuals recently diagnosed with the flu. Twenty-one of these individuals were given a placebo, and their average flu durations was 12.6 days (SD = 1.88). The remaining 21 subjects were given Tamiflu, and their average flu duration was 11.4 days (SD = 1.58). Did Tamiflu make reduce the duration of the flu? What is the effect size for this difference? state the null and alternavive hypthesis, aplha level of 0.05 please text the null hypthesis and draw the rejction regionarrow_forwardYou are concerned that nausea may be a side effect of Tamiflu, but you cannot just give Tamiflu to patients with the flu and say that nausea is a side effect if people become nauseous. This is because nausea is common for people who have the flu. From past studies you know that about 30% of people who get the flu experience nausea. You collected data on 1744 patients who were taking Tamiflu to relieve symtoms of the flu, and found that 572 experienced nausea. Use a 0.01 significance level to test the claim that the percentage of people who take Tamiflu for the relief of flu symtoms and experience nausea is greater than 30%.a) Identify the null and alternative hypotheses?�0: �1: b) What type of hypothesis test should you conduct (left-, right-, or two-tailed)? left-tailed right-tailed two-tailed c) Identify the appropriate significance level.d) Calculate your test statistic. Write the result below, and be sure to round your final answer to two decimal…arrow_forward
- Although arsenic is known to be a poison, it also has some beneficial medicinal uses. In one study of the use of arsenic to treat acute promyelocytic leukemia (APL), a rare type if blood cancer, APL patients were given an arsenic compound as part of their treatment. Of those receiving arsenic, 32% were in remission and showed no signs of leukemia in subsequent examination. It is known that 18% of APL patients go into remission after conventional treatment. Suppose that the study had included 100 randomly selected patients. Is there sufficient evidence to conclude that the proportion in remission for the arsenic treatment is greater than 0.18, the remission proportion for conventional treatment? a. Test the hypothesis at the 0.01 significance level. b. Construct and interpret a 99% confidence interval for the true proportion of APL patients who go into remission after using arsenic. Does the inference drawn from this interval match the conclusion from the test that you did in part…arrow_forwardYou are concerned that nausea may be a side effect of Tamiflu, but you cannot just give Tamiflu to patients with the flu and say that nausea is a side effect if people become nauseous. This is because nausea is common for people who have the flu. From past studies you know that about 32% of people who get the flu experience nausea. You collected data on 2494 patients who were taking Tamiflu to relieve symtoms of the flu, and found that 870 experienced nausea. Use a 0.01 significance level to test the claim that the percentage of people who take Tamiflu for the relief of flu symtoms and experience nausea is greater than 32%. a) Identify the null and alternative hypotheses? Ho: ? v Ha: ? v b) What type of hypothesis test should you conduct (left-, right-, or two-tailed)? O left-tailed O right-tailed O two-tailed c) Identify the appropriate significance level. Submit Question 3.arrow_forwardYou are concerned that nausea may be a side effect of Tamiflu, but you cannot just give Tamiflu to patients with the flu and say that nausea is a side effect if people become nauseous. This is because nausea is common for people who have the flu.Past studies state that about 33% of people who get the flu experience nausea. You collected data on 2248 patients who were taking Tamiflu to relieve symtoms of the flu, and found that 810 experienced nausea. You decide to carry out a simulation to test the claim that the percentage of people who take Tamiflu for the relief of flu symtoms and experience nausea is greater than 33%.a) Identify the null and alternative hypotheses.H0H0: ? p = p ≠ p < p > p ≤ p ≥ μ = μ ≠ μ < μ > μ ≤ μ ≥ H1H1: ? p = p ≠ p < p > p ≤ p ≥ μ = μ ≠ μ < μ > μ ≤ μ ≥arrow_forward
- You are concerned that nausea may be a side effect of Tamiflu, but you cannot just give Tamiflu to patients with the flu and say that nausea is a side effect if people become nauseous. This is because nausea is common for people who have the flu. From past studies you know that about 34% of people who get the flu experience nausea. You collected data on 1926 patients who were taking Tamiflu to relieve symtoms of the flu, and found that 711 experienced nausea. Use a 0.01 significance level to test the claim that the percentage of people who take Tamiflu for the relief of flu symtoms and experience nausea is greater than 34%. a) Identify the null and alternative hypotheses? Ho: ? H₁: ? b) What type of hypothesis test should you conduct (left-, right-, or two-tailed)? left-tailed right-tailed O two-tailed c) Identify the appropriate significance level. d) Calculate your test statistic. Write the result below, and be sure to round your final answer to two decimal places. e) Calculate your…arrow_forwardYou are concerned that nausea may be a side effect of Tamiflu, but you cannot just give Tamiflu to patients with the flu and say that nausea is a side effect if people become nauseous. This is because nausea is common for people who have the flu. From past studies you know that about 32% of people who get the flu experience nausea. You collected data on 1970 patients who were taking Tamiflu to relieve symtoms of the flu, and found that 683 experienced nausea. Use a 0.01 significance level to test the claim that the percentage of people who take Tamiflu for the relief of flu symtoms and experience nausea is greater than 32%. a) Identify the null and alternative hypotheses? Ho: ? H1: ? b) What type of hypothesis test should you conduct (left-, right-, or two-tailed)? O left-tailed right-tailed two-tailed c) Identify the appropriate significance level. d) Calculate your test statistic. Write the result below, and be sure to round your final answer to two decimal places. e) Calculate your…arrow_forwardA medical researcher wants to test the effectiveness of a new drug in treating a certain disease. They randomly assigned 100 patients to two groups: one group received the new drug, and the other group received a placebo. After a month, they measured the patients' symptom severity on a scale of 1 to 10. The researcher found that the mean symptom severity score for the group that received the new drug was lower than the mean score for the group that received the placebo. How can the researcher test the hypothesis that the new drug is effective in treating the disease? What statistical test should they use?arrow_forward
- Researchers Regine Dilla and associates wanted to determine whether consumption of cola is associated with lower bone mineral density. They looked at 1125 men and 1413 women in the Framingham Osteoporosis Study, which is a cohort that began in 1971. The first examination in this study began between 1971 and 1975, with participants returning for an examination every 4 years. Based on results of questionnaires, the researchers were able to determine cola consumption on a weekly basis. Analysis of the results indicated that women who consumed at least one cola per day (on average) had a bone mineral density that was significantly lower at the femoral neck than those who consumed less than one cola per day. The researchers did not find this relation in men. (a)Why is this a cohort study? (b)What is the response variable in this study? What is the explanatory variable? (c)Is the response variable qualitative or quantitative?arrow_forwardLung cancer is the leading cause of cancer‑related deaths in the United States. Researchers examined the idea of testing all Medicare‑enrolled heavy smokers for lung cancer with a computed tomography (CT) scan every year. In this population, the lifetime chance of developing lung cancer is high. In any given year, approximately 3%3% of heavy smokers develop lung cancer. The CT scan positively identifies lung cancer 89%89% of the time, and it gives a negative result for 93%93% of individuals who do not have lung cancer. (a) Use probability notation to express the three values cited. Match the notation with the appropriate values. Not necessarily all notation choices should be used.arrow_forwardMost cases of cervical cancer are linked to a few strains of the human papilloma virus (HPV). The pharmaceutical company Merck developed a vaccine (Gardisil) against these HPV strains. Worldwide clinical trials followed young women after vaccination or administration of placebo for two to four years for signs of HPV-caused cervical cancer. Based on a sample of 100 women in the Gardisil group, 24 % developed cervical cancer, and based on a sample of 100 women in the placebo group, 34 % developed cervical cancer. Test the claim that the proportion of women who developed cervical cancer in the Gardisil group is less than the proportion of women who developed cervical cancer in the placebo group at a = 0.10. Round your answers to three decimal places, and round any interim calculations to four decimal places. Fill in the hypotheses below where p₁ denotes the proportion of women who developed cervical cancer in the Gardisil group and p2 denotes the proportion of women who developed cervical…arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Hypothesis Testing - Solving Problems With Proportions; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=76VruarGn2Q;License: Standard YouTube License, CC-BY
Hypothesis Testing and Confidence Intervals (FRM Part 1 – Book 2 – Chapter 5); Author: Analystprep;https://www.youtube.com/watch?v=vth3yZIUlGQ;License: Standard YouTube License, CC-BY