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Ch. 9 - Inferences from Two Samples
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Triola 14th EditionCh. 9 - Inferences from Two Samples문제 9.R.6a
9장, 문제 9.R.6a

Smoking Cessation Programs


a. Construct the confidence interval that could be used to test the claim in Exercise 5. What feature of the confidence interval leads to the same conclusion from Exercise 5?

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Step 1: Identify the data and parameters needed to construct the confidence interval. Determine the sample mean (\( \bar{x} \)), sample size (\( n \)), standard deviation (\( s \) or \( \sigma \)), and the confidence level (e.g., 95%).
Step 2: Choose the appropriate formula for the confidence interval based on the data. If the population standard deviation (\( \sigma \)) is known, use the formula \( \bar{x} \pm Z \frac{\sigma}{\sqrt{n}} \). If \( \sigma \) is unknown, use \( \bar{x} \pm t \frac{s}{\sqrt{n}} \), where \( t \) is the critical value from the t-distribution.
Step 3: Calculate the margin of error using the formula \( Z \frac{\sigma}{\sqrt{n}} \) or \( t \frac{s}{\sqrt{n}} \), depending on whether \( \sigma \) is known or unknown. Ensure you use the correct critical value (\( Z \) or \( t \)) corresponding to the confidence level.
Step 4: Construct the confidence interval by adding and subtracting the margin of error from the sample mean (\( \bar{x} \)). The confidence interval will be \( [\bar{x} - \text{Margin of Error}, \bar{x} + \text{Margin of Error}] \).
Step 5: Interpret the confidence interval in the context of the claim from Exercise 5. If the confidence interval does not contain the value specified in the null hypothesis, it supports rejecting the null hypothesis. Conversely, if the interval contains the value, it supports failing to reject the null hypothesis.

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주요 개념

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Confidence Interval

A confidence interval is a range of values, derived from sample statistics, that is likely to contain the true population parameter with a specified level of confidence, typically 95% or 99%. It provides an estimate of uncertainty around a sample mean or proportion, allowing researchers to infer about the population. The width of the interval reflects the variability in the data and the sample size; larger samples yield narrower intervals.
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06:33
Introduction to Confidence Intervals

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about population parameters based on sample data. It involves formulating a null hypothesis (H0) and an alternative hypothesis (H1), then using sample data to determine whether to reject H0. The results of hypothesis tests can be supported by confidence intervals, as both approaches assess the likelihood of observing the data under the null hypothesis.
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가이드 코스
06:21
Step 1: Write Hypotheses

Margin of Error

The margin of error is a statistic that expresses the amount of random sampling error in a survey's results. It quantifies the uncertainty associated with the sample estimate, indicating how much the estimate could vary from the true population value. In the context of confidence intervals, the margin of error is half the width of the interval and is influenced by the sample size and variability in the data.
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04:08
Finding the Minimum Sample Size Needed for a Confidence Interval
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교과서 질문

Forecast and Actual Temperatures Listed below are actual temperatures (°F) along with the temperatures that were forecast five days earlier (data collected by the author). Use a 0.05 significance level to test the claim that differences between actual temperatures and temperatures forecast five days earlier are from a population with a mean of 0°F.

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교과서 질문

Test Values p_cap1, p_cap2. Find the values of and the pooled proportion p_bar obtained when testing the claim given in Exercise 1.

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교과서 질문

Body Temperatures Listed below are body temperatures from six different subjects measured at two different times in a day (from Data Set 5 “Body Temperatures” in Appendix B).


b. Identify the null and alternative hypotheses for using the sample data to test the claim that the differences between 8 AM temperatures and 12 AM temperatures are from a population with a mean equal to 0°F

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교과서 질문

Identifying Hypotheses In a randomized clinical trial of adults with an acute sore throat, 288 were treated with the drug dexamethasone and 102 of them experienced complete resolution; 277 were treated with a placebo and 75 of them experienced complete resolution (based on data from “Effect of Oral Dexamethasone Without Immediate Antibiotics vs Placebo on Acute Sore Throat in Adults,” by Hayward et al., Journal of the American Medical Association). Identify the null and alternative hypotheses corresponding to the claim that patients treated with dexamethasone and patients given a placebo have the same rate of complete resolution.

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교과서 질문

Variation of Hospital Times Use the sample data given in Exercise 7 “Seat Belts” and test the claim that for children hospitalized after motor vehicle crashes, the numbers of days in intensive care units for those wearing seat belts and for those not wearing seat belts have the same variation. Use a 0.05 significance level.

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교과서 질문

Smoking Cessation Programs Among 198 smokers who underwent a “sustained care” program, 51 were no longer smoking after six months. Among 199 smokers who underwent a “standard care” program, 30 were no longer smoking after six months (based on data from “Sustained Care Intervention and Postdischarge Smoking Cessation Among Hospitalized Adults,” by Rigotti et al., Journal of the American Medical Association, Vol. 312, No. 7). We want to use a 0.01 significance level to test the claim that the rate of success for smoking cessation is greater with the sustained care program. Test the claim using a hypothesis test.

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