identify test statisticidentify p-valueWhat is the confidence interval of p1-p2 ### Educational Content: Hypothesis Testing for Echinacea's Effectiveness#### BackgroundRhino viruses are known to cause common colds. A study was conducted to evaluate the effectiveness of echinacea in preventing rhinovirus infections. Of the 41 subjects treated with echinacea, 34 developed rhinovirus infections. In contrast, within a placebo group of 95 subjects, 81 developed rhinovirus infections. This analysis is performed at a 0.05 significance level to evaluate whether echinacea has a statistically significant effect on rhinovirus infection rates.#### Hypothesis Testing##### ObjectiveTest the claim regarding the effectiveness of echinacea using a hypothesis test.##### MethodologyConsider the first sample (treated with echinacea) and the second sample (treated with placebo).##### HypothesesSelect the appropriate null and alternative hypotheses for this test:- **Option D (Correct):** - \( H_0: p_1 = p_2 \) (The proportion of infections is the same in both groups) - \( H_1: p_1 \neq p_2 \) (The proportion of infections differs between the groups)##### Steps1. **Identify the Test Statistic:** - **Calculate the z-value** for comparing the proportions of the two independent samples. - **Round the test statistic to two decimal places as needed.**This setup allows for the evaluation of whether echinacea significantly alters the rate of rhinovirus infection compared to a placebo.

Null hypothesis is not rejected

Answered: Rhino viruses typically cause common…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Rock band The Rolling Stones have played scores of concerts in the last twenty years. For 30 randomly selected Rolling Stones concerts, the mean gross earnings is 2.18 million dollars. Part a) Assuming a population standard deviation gross earnings of 0.53 million dollars, obtain a 99% confidence interval for the mean gross earnings of all Rolling Stones concerts (in millions).Confidence interval: ( , ). Part b)Which of the following is the correct interpretation for your answer in part (a)?A. If we repeat the study many times, 99% of the calculated confidence intervals will contain the mean gross earning of all Rolling Stones concerts.B. We can be 99% confident that the mean gross earnings for this sample of 30 Rolling Stones concerts lies in the intervalC. There is a 99% chance that the mean gross earnings of all Rolling Stones concerts lies in the intervalD. None of the above
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In a study of speed dating, male subjects were asked to rate the attractiveness of their female dates, and a sample of the results is listed below (1=not attractive; 10=extremely attractive). A) Construct a confidence interval using a 95% confidence level. What do the results tell about the mean attractiveness ratings of the population of all adult females? 7, 9, 3, 10, 6, 4, 6, 9, 9, 10, 4, 8 What is the confidence interval for the population mean μ? ___<μ<___. (Round to one decimal place as needed.) B) What does the confidence intervcal tell us about the population of all adult females? Select the choices below. A. We are 95 percent confident that the interval from ___ to ___ actually contains the true mean attractiveness rating of all adult females. (Round to one decimal place as needed). B. The results tell nothing about the population of all adult females, because participants in speed dating are not a representative sample of all adult…
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What statement is incorrect regarding the z-statistic and the z-critical when taking a sample in order to estimate the Mean of a population? The z-statistic is the z-value determined by subtracting the hypothesis mean from the mean of the sample data and dividing by the standard error The standard error is the standard deviation divided by the square root of the # of sample points z-critical is at the edges of the confidence interval: negative z-critical is the left edge and positive z-critical is the right edge If a positive z-statistic is less than the positive z-critical, we reject the Null hypothesis
Rock band The Rolling Stones have played scores of concerts in the last twenty years. For 30 randomly selected Rolling Stones concerts, the mean gross earnings is 2.18 million dollars. Part a) Assuming a population standard deviation gross earnings of 0.53 million dollars, obtain a 99% confidence interval for the mean gross earnings of all Rolling Stones concerts (in millions).Confidence interval: ( , ). Part b)Which of the following is the correct interpretation for your answer in part (a)?A. If we repeat the study many times, 99% of the calculated confidence intervals will contain the mean gross earning of all Rolling Stones concerts.B. We can be 99% confident that the mean gross earnings for this sample of 30 Rolling Stones concerts lies in the intervalC. There is a 99% chance that the mean gross earnings of all Rolling Stones concerts lies in the intervalD. None of the above
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A random sample of 17 subjects was asked to perform a given task. The time in seconds it took each of them to complete the task is recorded below. 47, 50, 40, 40, 48, 44, 39, 29, 34, 47, 27, 46, 46, 45, 47, 27, 35 Send data to calculator Send data to Excel If we assume that the completion times are normally distributed, find a 95% confidence interval for the true mean completion time for this task. Then find the lower limit and upper limit of the 95% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.) Lower limit: | Upper limit:I

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