Finding Critical Values and Confidence Intervals. In Exercises 5–8, use the given information to find the number of degrees of freedom, the critical values
5. Nicotine in Menthol Cigarettes 95% confidence; n = 25, s = 0.24 mg.
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- Heart rate during laughter. Laughter is often called “the best medicine,” since studies have shown that laughter can reduce muscle tension and increase oxygenation of the blood. In the International Journal of Obesity (Jan. 2007), researchers at Vanderbilt University investigated the physiological changes that accompany laughter. Ninety subjects (18–34 years old) watched film clips designed to evoke laughter. During the laughing period, the researchers measured the heart rate (beats per minute) of each subject, with the following summary results: Mean = 73.5, Standard Deviation = 6. n=90 (we can treat this as a large sample and use z) It is well known that the mean resting heart rate of adults is 71 beats per minute. Based on the research on laughter and heart rate, we would expect subjects to have a higher heart beat rate while laughing.Construct 95% Confidence interval using z value. What is the lower bound of CI? a) Calculate the value of the test statistic.(z*) b) If…arrow_forwardExercise 2.1 (Sample Space and Events) The rise times (unit: min.) of a reactor for two batches are measured in an experiment. 1. Define the sample space of the experiment. 2. Define Ei where the reactor rise time of the first batch is less than 55 min. and E2 where the reactor rise time of the second batch is greater than 70 min. 3. Find E¡ U E2, Ei N E2, and Ei'. 4. Are Ei and E2 mutually exclusive? 5. Are Ei and E2 exhaustive? Engr. A. CUH-INGarrow_forwardLarge Data Sets from Appendix B. In Exercises 25–28, use the data set from Appendix B to test the given claim. Use the P-value method unless your instructor specifies otherwise. Diastolic Blood Pressure for Men Repeat the preceding exercise for adult males instead of adult females.arrow_forward
- P -Values. In Exercises 17–20, do the following: a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed. b. Find the P-value. (See Figure 8-3 on page 364.) c. Using a significance level of α = 0.05, should we reject H0 or should we fail to reject H0? The test statistic of z = 2.01 is obtained when testing the claim that p ≠ 0.345.arrow_forwardAspirin II: Safety Considerations Regarding the experiment in the data frame Aspirin from the abd package, the researchers wanted to know whether or not taking aspirin affects one's risk of developing cancer. Recall that they defined their parameters as follows: p1 = the proportion of ALL individuals who would develop cancer, if all of them were to take aspirin like the subjects in the Aspirin group did. p2 = the proportion of ALL individuals who would develop cancer, if all of them were to take a placebo, like the subjects in the placebo group did. They ran the code for a two-sided significance test and got the following results: ## ## ## Inferential Procedures for the Difference of Two Proportions p1-p2:## cancer grouped by treatment ## ## ## Descriptive Results:## ## yes n estimated.prop## Aspirin 1438 19934 0.07214## Placebo 1427 19942 0.07156## ## ## Inferential Results:## ## Estimate of p1-p2: 0.0005805 ## SE(p1.hat - p2.hat): 0.002586 ## ## 95%…arrow_forwardIs this correct so far?arrow_forward
- Aspirin III: Decision and Conclusion Regarding the experiment in the data frame Aspirin from the abd package, the researchers wanted to know whether or not taking aspirin affects one's risk of developing cancer. Recall that they defined their parameters as follows: p1 = the proportion of ALL individuals who would develop cancer, if all of them were to take aspirin like the subjects in the Aspirin group did. p2 = the proportion of ALL individuals who would develop cancer, if all of them were to take a placebo, like the subjects in the placebo group did. They ran the code for a two-sided significance test and got the following results: ## ## ## Inferential Procedures for the Difference of Two Proportions p1-p2:## cancer grouped by treatment ## ## ## Descriptive Results:## ## yes n estimated.prop## Aspirin 1438 19934 0.07214## Placebo 1427 19942 0.07156## ## ## Inferential Results:## ## Estimate of p1-p2: 0.0005805 ## SE(p1.hat - p2.hat): 0.002586 ## ##…arrow_forwardT= , df=arrow_forwardExercise 2.1 (Sample Space and Events) The rise times (unit: min.) of a reactor for two batches are measured in an experiment. Define the sample space of the experiment. Define E1 where the reactor rise time of the first batch is less than 55 min. and E2 where the reactor rise time of the second batch is greater than 70 min. Find E1 E2, E1 E2, and E1’ Are E1 and E2 mutually exclusive? Are E1 and E2 exhaustive?arrow_forward
- Using the difference table provided, calculate the t statistic, the degree of freedom and the critical t value (s) of the sample.arrow_forwardTourism is extremely important to the economy of Florida. Hotel occupancy is an often-reported measure of visitor volume and visitor activity (Orlando Sentinel, May 19, 2018). Hotel occupancy data for February in two consecutive years are as follows. Occupied Rooms Total Rooms Current Year Let pi population proportion of rooms occupied for current year P = population proportion of rooms occupied for previous year 1,435 1,750 Previous Year a. Formulate the hypothesis test that can be used to determine whether there has been an increase in the proportion of rooms occupied over the one-year period. Ho Pi-Pa-Select your answer- H.: P-P-Select your answer- b. What is the estimated proportion of hotel rooms occupied each year (to 2 decimals)? 1,404 1,800 Current year Previous Year c. Conduct a hypothesis test. What is the p-value (to 4 decimals)? Use Table 1 from Appendix B. p-value- Using a 0.05 level of significance, what is your conclusion? We Select your answer that there has been an…arrow_forwardAge According to the Bureau of Labor Statistics, the average age of American workers is 41.9 years. The manager of a large technology company believes that the company's employees tend to be younger, on average. So she takes a random sample of 12 employees and records their ages. Here are the data: 27 38 32 24 30 47 42 38 27 43 37 33 a. State appropriate hypotheses for testing the manager's belief. Be sure to define the parameter of interest. b. State the conditions for performing a test of the hypotheses in (a), and determine whether each condition is met. c. The P-value of the test is 0.003. Interpret this value. What conclusion would you make?arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill