Ch. 8 - Hypothesis Testing with Two Samples

Larson - Elementary Statistics: Picturing the World 8th Edition

Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470당신이 사용하는 게 아니라요?교과서 변경

Larson 8th Edition

Ch. 8 - Hypothesis Testing with Two Samples

문제 8.U.1

8장, 문제 8.U.1

Confounding Variables A pharmaceutical company has applied for approval to market a new arthritis medication. The research involved a test group that was given the medication and another test group that was given a placebo. Describe some possible confounding variables that could influence the results of the study.

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Understand the concept of confounding variables: A confounding variable is an external factor that influences both the independent variable (medication or placebo) and the dependent variable (effectiveness of the treatment), potentially distorting the results of the study.

Identify demographic factors: Age, gender, and ethnicity of participants could act as confounding variables if they are unevenly distributed between the test and placebo groups, as these factors may influence how individuals respond to the medication.

Consider health-related factors: Pre-existing conditions, severity of arthritis, or other medications being taken by participants could impact the effectiveness of the treatment and introduce bias into the results.

Evaluate lifestyle factors: Diet, exercise habits, and stress levels could also act as confounding variables, as they may affect the participants' overall health and response to the medication.

Assess environmental factors: Differences in living conditions, access to healthcare, or geographic location could influence the results, as these factors may affect participants' health outcomes independently of the medication or placebo.

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Confounding Variables

Confounding variables are extraneous factors that can influence both the independent and dependent variables in a study, potentially leading to erroneous conclusions. In the context of the arthritis medication study, these could include factors like age, gender, or pre-existing health conditions that might affect the participants' responses to the medication or placebo.

Randomization

Randomization is a technique used in experimental studies to assign participants to different groups in a way that minimizes bias. By randomly assigning individuals to either the medication or placebo group, researchers can help ensure that confounding variables are evenly distributed across both groups, thus enhancing the validity of the study's results.

Blinding

Blinding refers to the practice of keeping study participants and/or researchers unaware of which participants are receiving the treatment or placebo. This method helps to reduce bias in reporting and assessing outcomes, as it prevents expectations from influencing the results. In the arthritis medication study, double-blinding would mean neither the participants nor the researchers know who is receiving the actual medication.

관련 실천

교과서 질문

Take this test as you would take a test in class.For each exercise, perform the steps below.

b.Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed, and whether to use a z-test or a t-test. Explain your reasoning.

A real estate agency says that the mean home sales price in Olathe, Kansas, is greater than in Rolla, Missouri. The mean home sales price for 39 homes in Olathe is \$392,453. Assume the population standard deviation is \$224,902. The mean home sales price for 38 homes in Rolla is \$285,787. Assume the population standard deviation is \$330,578. At α=0.05, is there enough evidence to support the agency’s claim? (Adapted from Realtor.com)

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교과서 질문

Find the critical value(s) for the alternative hypothesis, level of significance , and sample sizes and . Assume that the samples are random and independent, the populations are normally distributed, and the population variances are (a) equal

Ha:μ1≠μ2 , α=0.10 , n1=11 , n2=14

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교과서 질문

Testing the Difference Between Two Means (a) identify the claim and state Ho and Ha .Assume the samples are random and dependent, and the populations are normally distributed.

[APPLET] Passing Play Percentages The passing play percentages of 10 randomly selected NCAA Division 1A college football teams for home and away games in the 2020–2021 season are shown in the table. At , α=0.20 is there enough evidence to support the claim that passing play percentage is different for home and away games? (Source: TeamRankings)

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교과서 질문

In Exercises 4 and 5, use technology to perform a two-sample t-test to determine whether there is a difference in the mint dates and in the values of coins found on a street from 1985 through 1996 for the two mint locations. Write your conclusion as a sentence. Use α = 0.05.

Mint dates of coins (years)

Philadelphia: x̅1=1984.8, s1=8.6

Denver: x̅2=1983.4, s2=8.4

Assume population variances are equal.

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교과서 질문

Take this test as you would take a test in class.For each exercise, perform the steps below.

a. Identify the claim and state and

b.Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed, and whether to use a z-test or a t-test. Explain your reasoning.

c.Find the critical value(s) and identify the rejection region(s).

d. Find the appropriate standardized test statistic.

e. Decide whether to reject or fail to reject the null hypothesis.

f. Interpret the decision in the context of the original claim.

A demographics researcher claims that the mean household income in a recent year is different for native-born households and foreign-born households. A sample of 18 native-born households has a mean household income of \$69,474 and a standard deviation of $21,249. A sample of 21 foreign-born households has a mean household income of $64,900 and a standard deviation of \$17,896. At α=0.01, can you support the demographics researcher’s claim? Assume the populations are normally distributed and the population variances are not equal. (Adapted from U.S. Census Bureau)

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교과서 질문

Testing the Difference Between Two Means (a) identify the claim and state Ho and Ha

[APPLET] Migraines

A researcher claims that injections of onabotulinumtoxinA reduce the number of days per month that chronic migraine sufferers have headaches. The table shows the number of days chronic migraine sufferers suffered migraines before and after using the treatment. At , α= 0.01 is there enough evidence to support the researcher’s claim? (Adapted from Journal of Headache and Pain)

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