Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

In the experiment described in the paper "Exposure to Diesel Exhaust Induces Changes in EEG in Human Volunteers" (Particle and Fibre Toxicology [2007])\(, 10\) healthy men were exposed to diesel exhaust for 1 hour. A measure of brain activity (called median power frequency, or MPF) was recorded at two different locations in the brain both before and after the diesel exhaust exposure. The resulting data are given in the accompanying table. For purposes of this example, assume that it is reasonable to regard the sample of 10 men as representative of healthy adult males. $$ \begin{array}{ccrcr} \hline & \text { Location 1 } & \text { Location 1 } & \text { Location 2 } & \text { Location 2 } \\ \text { Subject } & \text { Before } & \text { After } & \text { Before } & \text { After } \\ \hline 1 & 6.4 & 8.0 & 6.9 & 9.4 \\ 2 & 8.7 & 12.6 & 9.5 & 11.2 \\ 3 & 7.4 & 8.4 & 6.7 & 10.2 \\ 4 & 8.7 & 9.0 & 9.0 & 9.6 \\ 5 & 9.8 & 8.4 & 9.7 & 9.2 \\ 6 & 8.9 & 11.0 & 9.0 & 11.9 \\ 7 & 9.3 & 14.4 & 7.9 & 9.1 \\ 8 & 7.4 & 11.3 & 8.3 & 9.3 \\ 9 & 6.6 & 7.1 & 7.2 & 8.0 \\ 10 & 8.9 & 11.2 & 7.4 & 9.1 \\ \hline \end{array} $$ a. Do the data provide convincing evidence that the mean MPF at brain location 1 is higher after diesel exposure? Test the relevant hypotheses using a significance level of \(.05 .\) b. Construct and interpret a \(90 \%\) confidence interval estimate for the difference in mean MPF at brain location 2 before and after exposure to diesel exhaust.

Short Answer

Expert verified
For part a, the conclusion depends on the p-value from the computation in Step 3. If the p-value is less than 0.05, then there is convincing evidence to suggest that the mean MPF at brain location 1 is higher after diesel exposure. For part b, the interpretation will depend on the constructed 90% confidence interval in Step 4. If the interval includes 0, there's no significant effect of diesel exposure on the mean MBF at brain location 2, but if 0 is not in the interval, it suggests a significant effect.

Step by step solution

01

State the hypotheses

The null hypothesis (H0) is that the mean MPF is the same before and after diesel exposure. The alternative hypothesis (Ha) is that the mean MPF is higher after diesel exposure. H0: µ_before = µ_after, Ha: µ_before < µ_after. Remember, µ_before represents the mean MBF at a specific brain location before diesel exposure and µ_after represents the mean MBF after diesel exposure.
02

Compute the test statistic

First, compute the mean and standard deviation of the differences in MBF before and after diesel exposure for both locations. Use these to compute the t test statistic: t = (Xbar - µ) / (s/√n), where Xbar is the sample mean, µ is the population mean under H0, s is the standard deviation of the sample, and n is the sample size.
03

Compute the p-value and reach a decision

Use a t-distribution to compute the p-value corresponding to the absolute value of the t statistic. If the p-value is less than 0.05, the significance level, then reject the null hypothesis.
04

Compute the confidence interval

For part b, to prepare the 90% confidence interval for the difference in mean MBF at brain location 2 before and after exposure, use this formula: (Xbar_diff - t*s/√n , Xbar_diff + t*s/√n), where Xbar_diff is the mean of the differences, s is the standard deviation of the differences, and n is the sample size. 't' is the t critical value for a 90% confidence level, which can be found in a t-table.
05

Interpret the confidence interval

The 90% confidence interval provides a range of plausible values for the mean difference in MBF before and after diesel exposure at brain location 2. If the interval includes 0, that suggests no significant effect of diesel exposure. If 0 is not in the interval, it suggests a significant effect.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Mean Power Frequency
When studying brain activity, one important measure researchers use is the Mean Power Frequency (MPF). MPF represents the average frequency at which the power of the electrical signals generated by the brain is highest. In simpler terms, it is a method to quantify the activity in different parts of the brain under various conditions.

MPF is particularly useful in neuroscience and psychology research, as changes in MPF may indicate alterations in neuronal activity, possibly due to exposure to certain stimuli or substances, such as diesel exhaust in the given exercise. By comparing MPF measurements taken at different times, such as before and after exposure, scientists can infer whether an external factor has a significant effect on brain function.
Confidence Interval Estimation
Understanding confidence interval estimation is crucial when dealing with statistics. A confidence interval gives a range within which we are fairly sure the true parameter (like the mean power frequency difference) lies. It's calculated from the data and has a corresponding confidence level, like 90%, which in plain language means 'we're 90% confident that the true difference between MPFs before and after exposure is within this interval'.

When constructing confidence intervals, you use the mean of your sample measurements and adjust for variability and sample size. The interval adds and subtracts a margin of error from the sample mean, which includes the t critical value from the t-distribution reflecting the level of confidence you're aiming for.
t-test
The t-test is a statistical method used to determine if there is a significant difference between the means of two groups, under the assumption that the populations follow a normal distribution. In the context of our exercise, a t-test helps us test the hypothesis that the mean power frequency at specific brain locations has changed after exposure to diesel exhaust.

The t-test calculates a 't statistic', which, in essence, shows how much the sample mean deviates from the null hypothesis' expected mean, scaled by the variability of the data. A p-value is then derived from this t statistic, which gives the probability of observing such a difference if the null hypothesis were true. A p-value lower than the chosen significance level, like .05, indicates strong evidence against the null hypothesis, suggesting that the diesel exposure had a significant effect on MPF.
Brain Activity Measurement
Assessing brain activity involves various techniques, and measuring the mean power frequency (MPF) is one of them. MPF captures the electrical activity in the brain, which can be recorded using electroencephalography (EEG). During EEG, electrodes placed on the scalp detect the brain's electrical signals, and these readings allow researchers to explore how different factors, like environmental pollutants, may affect mental states and cognitive functions.

This type of measurement is highly relevant in studies like the one mentioned in the exercise because it provides direct insight into the physiological effects that substances, such as diesel exhaust, can have on the brain. By evaluating the MPF changes, scientists gather evidence on how certain exposures can influence neuronal dynamics, potentially leading to recommendations for public health or workplace safety.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The report "Audience Insights: Communicating to Teens (Aged 12-17)" (www.cdc.gov, 2009) described teens' attitudes about traditional media, such as TV, movies, and newspapers. In a representative sample of American teenage girls, \(41 \%\) said newspapers were boring. In a representative sample of American teenage boys, \(44 \%\) said newspapers were boring. Sample sizes were not given in the report. a. Suppose that the percentages reported had been based on a sample of 58 girls and 41 boys. Is there convincing evidence that the proportion of those who think that newspapers are boring is different for teenage girls and boys? Carry out a hypothesis test using \(\alpha=.05\) b. Suppose that the percentages reported had been based on a sample of 2000 girls and 2500 boys. Is there convincing evidence that the proportion of those who think that newspapers are boring is different for teenage girls and boys? Carry out a hypothesis test using \(\alpha=.05\). c. Explain why the hypothesis tests in Parts (a) and (b) resulted in different conclusions.

The paper "The Psychological Consequences of Money" (Science [2006]: \(1154-1156\) ) describes several experiments designed to investigate the way in which money can change behavior. In one experiment, participants completed one of two versions of a task in which they were given lists of five words and were asked to rearrange four of the words to create a sensible phrase. For one group, half of the 30 unscrambled phrases related to money, whereas the other half were phrases that were unrelated to money. For the second group (the control group), none of the 30 unscrambled phrases related to money. Participants were 44 students at Florida State University. Participants received course credit and \(\$ 2\) for their participation. The following description of the experiment is from the paper: Participants were randomly assigned to one of two conditions, in which they descrambled phrases that primed money or neutral concepts. Then participants completed some filler questionnaires, after which the experimenter told them that the experiment was finished and gave them a false debriefing. This step was done so that participants would not connect the donation opportunity to the experiment. As the experimenter exited the room, she mentioned that the lab was taking donations for the University Student Fund and that there was a box by the door if the participant wished to donate. Amount of money donated was the measure of helping. We found that participants primed with money donated significantly less money to the student fund than participants not primed with money \([t(38)=2.13, P<0.05]\) The paper also gave the following information on amount donated for the two experimental groups. a. Explain why the random assignment of participants to experimental groups is important in this experiment. b. Use the given information to verify the values of the test statistic and degrees of freedom (38, given in parentheses just after the \(t\) in the quote from the paper) and the statement about the \(P\) -value. Assume that both sample sizes are 22 . c. Do you think that use of the two-sample \(t\) test was appropriate in this situation? Hint: Are the assumptions required for the two-sample \(t\) test reasonable?

A hotel chain is interested in evaluating reservation processes. Guests can reserve a room by using either a telephone system or an online system that is accessed through the hotel's web site. Independent random samples of 80 guests who reserved a room by phone and 60 guests who reserved a room online were selected. Of those who reserved by phone, 57 reported that they were satisfied with the reservation process. Of those who reserved online, 50 reported that they were satisfied. Based on these data, is it reasonable to conclude that the proportion who are satisfied is higher for those who reserve a room online? Test the appropriate hypotheses using \(\alpha=.05\)

Some commercial airplanes recirculate approximately \(50 \%\) of the cabin air in order to increase fuel efficiency. The authors of the paper "Aircraft Cabin Air Recirculation and Symptoms of the Common Cold" (Journal of the American Medical Association [2002]: \(483-486\) ) studied 1100 airline passengers who flew from San Francisco to Denver between January and April 1999\. Some passengers traveled on airplanes that recirculated air and others traveled on planes that did not recirculate air. Of the 517 passengers who flew on planes that did not recirculate air, 108 reported post-flight respiratory symptoms, while 111 of the 583 passengers on planes that did recirculate air reported such symptoms. Is there sufficient evidence to conclude that the proportion of passengers with post-flight respiratory symptoms differs for planes that do and do not recirculate air? Test the appropriate hypotheses using \(\alpha=.05\). You may assume that it is reasonable to regard these two samples as being independently selected and as representative of the two populations of interest.

"Doctors Praise Device That Aids Ailing Hearts" (Associated Press, November 9,2004 ) is the headline of an article that describes the results of a study of the effectiveness of a fabric device that acts like a support stocking for a weak or damaged heart. In the study, 107 people who consented to treatment were assigned at random to either a standard treatment consisting of drugs or the experimental treatment that consisted of drugs plus surgery to install the stocking. After two years, \(38 \%\) of the 57 patients receiving the stocking had improved and \(27 \%\) of the patients receiving the standard treatment had improved. Do these data provide convincing evidence that the proportion of patients who improve is higher for the experimental treatment than for the standard treatment? Test the relevant hypotheses using a significance level of \(.05 .\)

See all solutions

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free