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Ch. 9 - Inferences from Two Samples
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
All textbooksTriola 14th EditionCh. 9 - Inferences from Two SamplesProblem 9.3.3c
Chapter 9, Problem 9.3.3c

Confidence Interval Assume that we want to use the sample data in Exercise 1 for constructing a confidence interval to be used for testing the given claim.


c. If the resulting confidence interval is -5.8 admissions <ud < -0.9 admissions, what do you conclude?

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1
Understand the problem: The confidence interval provided is -5.8 < μd < -0.9, where μd represents the population mean difference. The goal is to interpret this interval in the context of the claim being tested.
Recall the meaning of a confidence interval: A confidence interval provides a range of plausible values for the population parameter (in this case, μd). If the interval does not include 0, it suggests that there is a statistically significant difference.
Analyze the interval: Since the entire confidence interval (-5.8 to -0.9) is below 0, this indicates that the population mean difference μd is likely negative. This suggests that there is evidence of a decrease in admissions.
Relate the interval to the claim: If the claim being tested is that there is no difference in admissions (μd = 0), the confidence interval contradicts this claim because 0 is not within the interval. This means we reject the null hypothesis.
Conclude: Based on the confidence interval, there is sufficient evidence to support the conclusion that there is a significant decrease in admissions.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Confidence Interval

A confidence interval is a range of values derived from sample data that is likely to contain the true population parameter. It is expressed with a lower and upper bound, indicating the degree of uncertainty around the estimate. For example, a 95% confidence interval suggests that if we were to take many samples, approximately 95% of the intervals calculated would contain the true parameter.
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Negative Values in Context

In the context of admissions, negative values in a confidence interval indicate a decrease in admissions rather than an increase. This can suggest that the actual number of admissions is likely to be lower than a certain threshold, which may have implications for decision-making in areas such as resource allocation or program effectiveness.
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Statistical Significance

Statistical significance refers to the likelihood that a result or relationship observed in data is not due to random chance. In the context of a confidence interval, if the interval does not include zero, it suggests that the effect being measured (e.g., change in admissions) is statistically significant, leading to a conclusion that the effect is likely real and not a result of sampling variability.
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Related Practice
Textbook Question

Overlap of Confidence Intervals In the article “On Judging the Significance of Differences by Examining the Overlap Between Confidence Intervals,” by Schenker and Gentleman (American Statistician, Vol. 55, No. 3), the authors consider sample data in this statement: “Independent simple random samples, each of size 200, have been drawn, and 112 people in the first sample have the attribute, whereas 88 people in the second sample have the attribute.”


c. Use a 0.05 significance level to test the claim that the two population proportions are equal. What do you conclude?


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Textbook Question

In Exercises 5–20, assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. (Note: Answers in Appendix D include technology answers based on Formula 9-1 along with “Table” answers based on Table A-3 with df equal to the smaller of n1-1 and n2-1)


Magnet Treatment of Pain People spend around \$5 billion annually for the purchase of magnets used to treat a wide variety of pains. Researchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured using the visual analog scale, and the results given below are among the results obtained in the study (based on data from “Bipolar Permanent Magnets for the Treatment of Chronic Lower Back Pain: A Pilot Study,” by Collacott, Zimmerman, White, and Rindone, Journal of the American Medical Association, Vol. 283, No. 10). Higher scores correspond to greater pain levels.


c. Does it appear that magnets are effective in treating back pain? Is it valid to argue that magnets might appear to be effective if the sample sizes are larger?


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Textbook Question

Can Dogs Detect Malaria? A study was conducted to determine whether dogs could detect malaria from socks worn by malaria patients and socks worn by patients without malaria. Among 175 socks worn by malaria patients, the dogs made correct identifications 123 times. Among 145 socks worn by patients without malaria, the dogs made correct identifications 131 times (based on data presented at an annual meeting of the American Society of Tropical Medicine, by principal investigator Steve Lindsay). Use a 0.05 significance level to test the claim of no difference between the two rates of correct responses.


c. What do the results suggest about the use of dogs to detect malaria?

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Textbook Question

In Exercises 5–16, use the listed paired sample data, and assume that the samples are simple random samples and that the differences have a distribution that is approximately normal.


Heights of Presidents A popular theory is that presidential candidates have an advantage if they are taller than their main opponents. Listed are heights (cm) of presidents along with the heights of their main opponents (from Data Set 22 “Presidents” in Appendix B).


b. Construct the confidence interval that could be used for the hypothesis test described in part (a). What feature of the confidence interval leads to the same conclusion reached in part (a)?

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Textbook Question

Clinical Trials of OxyContin OxyContin (oxycodone) is a drug used to treat pain, but it is well known for its addictiveness and danger. In a clinical trial, among subjects treated with OxyContin, 52 developed nausea and 175 did not develop nausea. Among other subjects given placebos, 5 developed nausea and 40 did not develop nausea (based on data from Purdue Pharma L.P.). Use a 0.05 significance level to test for a difference between the rates of nausea for those treated with OxyContin and those given a placebo.


c. Does nausea appear to be an adverse reaction resulting from OxyContin?

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Textbook Question

F Test Statistic


c. If testing the claim that sigma2,1 is not equals to sigma2,2 what do we know about the two samples if the test statistic F is very close to 1?


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