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
Videos
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 solution
Students 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?
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%.
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 32% of people who get the flu experience nausea. You collected data on 2254 patients who were taking Tamiflu to relieve symtoms of the flu, and found that 778 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%. d) Calculate your test statistic. Write the result below, and be sure to round your final answer to two decimal places.e) Calculate your p-value. Write the result below, and be sure to round your final answer to four decimal places.f) Do you reject the null hypothesis? We reject the null hypothesis, since the p-value is less than the significance level. We…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 2254 patients who were taking Tamiflu to relieve symtoms of the flu, and found that 778 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?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 ≥ 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…arrow_forwardResearchers wanted to know the effectiveness of a new anti-venom shot. A study was conducted on 245 children who had nonlethal scorpion stings. The ages of the children ranged from 6 months to 18 years old. Each child was randomly assigned to receive a shot of the anti-venom or a placebo shot. Researchers recorded whether or not their condition improved over the next four hours. They found that about 73% of the children who were given anti-venom saw an improvement in their condition whereas only about 23% of the children who were given the placebo saw an improvement in their condition. Identify the population.The population is all children 6 months to 18 years old with nonlethal scorpion stings. Identify the sample.The sample is 245 children 6 months to 18 years old with nonlethal scorpion stings. What is the treatment variable? The treatment variable is the anti-venom shot. What is the response (or outcome) variable?The outcome variable is improvements in their condition.…arrow_forward
- A 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_forwardIn elderly Americans, a new blood test is being developed to diagnose a particular disease. Suppose the sensitivity of this test is 80% and specificity is 70%. If it is known that 25% of them have the particular disease, then calculate the negative predictive value.arrow_forwardAlthough 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_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 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_forwardThe impact of a low-calorie diet on laboratory mice's longevity is being investigated by a medical researcher. Twenty mice are split into two groups (E and F) by random. A typical diet is given to Group E, while Group F is given a diet that only contains 70% as many calories as Group E's diet. The length of life (in days) of each mouse over the 36-month trial is documented. Table 2 provides the data that was obtained. The symbol of double star (**) signifies that the mouse was still alive at the end of the investigation. (a) (b) (c) Table 2: The length of life (in days) of each mouse Group E 900 907 751 833 920 787 830 877 848 901 Group F 1037 905 1023 988 1078 1011 ** 1063 898 1033 State a suitable null and alternative hypotheses for the problem. At 5% significance level, test the hypotheses in part (a) by using an appropriate nonparametric test. Write your conclusion.arrow_forwardA study is conducted to test a new drug claimed to reduce diastolic blood pressure in adults with a history of coronary heart disease. What is the most efficient study to test whether the drug reduces diastolic blood pressure?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 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_forwardA medical student at a community college in city Q wants to study the factors affecting the systolic blood pressure of a person (Y). Generally, the systolic blood pressure depends on the BMI of a person (B) and the age of the person A. She wants to test whether or not the BMI has a significant effect on the systolic blood pressure, keeping the age of the person constant. For her study, she collects a random sample of 150 patients from the city and estimates the following regression function: Y= 15.50 +0.90B + 1.10A. (0.48) (0.35) The test statistic of the study the student wants to conduct (Ho: B, =0 vs. H4: B, #0), keeping other variables constant is. (Round your answer to two decimal places.) At the 5% significance level, the student will v the null hypothesis. Keeping BMI constant, she now wants test whether the age of a person (A) has no significant effect or a positive effect on the person's systolic blood pressure. So, the test statistic associated with the one-sided test the…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
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