/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 27 When research chemists perform e... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

When research chemists perform experiments, they may obtain slightly different results on different replications, even when the experiment is performed identically each time. These differences are due to a phenomenon called "measurement error." a. List some variables in a chemical experiment that might cause some small changes in the final response measurement. b. If you want to make sure that your measurement error is small, you can replicate the experiment and take the sample average of all the measurements. To decrease the amount of variability in your average measurement, should you use a large or a small number of replications? Explain.

Short Answer

Expert verified
Answer: Some variables that might cause small changes in a chemical experiment's final response measurement include temperature, concentration of reactants, humidity, instrumentation error, and human error. To decrease the variability in the average measurement, a large number of replications should be used, as this allows random errors to cancel out and the average measurement to become closer to the true value.

Step by step solution

01

Part a: Identifying variables in a chemical experiment causing small changes in measurements

Some variables in a chemical experiment that might cause small changes in the final response measurement are: 1. Temperature: Even slight changes in temperature can affect the reaction rates, causing differences in the final response measurements. 2. Concentration of reactants: Small variations in the concentration of reactants can impact the overall reaction and lead to changes in the final measurements. 3. Humidity: Changes in humidity might affect some of the chemicals used in the experiment and cause deviations in the results. 4. Instrumentation error: The accuracy and precision of the measuring instruments used, such as pipettes, balances, and spectrometers, can introduce errors in the measurements. 5. Human error: Any small mistake made by the researcher, such as improper handling of the equipment, can introduce errors in the measurements.
02

Part b: Determining the appropriate number of replications to decrease variability

To decrease the amount of variability in the average measurement, you should use a large number of replications. The reason for this is that, when you perform a large number of replications, the random errors tend to cancel out, and the average measurement becomes closer to the true value. As you increase the number of replications, the variability in the average measurement decreases, leading to a more accurate and precise result.

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 91Ó°ÊÓ!

Key Concepts

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

Chemistry Experiment Variables
In a chemistry experiment, various factors can subtly alter the outcome, even when the procedure is performed identically. One major variable is temperature; even slight variations can impact reaction rates and affect the results. Another important variable is the concentration of reactants, where tiny differences can lead to noticeable changes in the outcome. Humidity can also play a role by interacting with the chemicals used, especially in reactions sensitive to moisture.

Moreover, instrumentation error is another common variable. Measuring instruments, like pipettes or balances, have their limits and slight deviations might occur. Lastly, human error is an ever-present factor, where improper handling or measurement can introduce discrepancies in results. Recognizing these variables is crucial for understanding how they can influence experimental data and ultimately impact the measurement accuracy.
Replication in Experiments
Replication is the key to minimizing the impact of random errors and improving the reliability of results in an experiment. When you replicate an experiment multiple times, each trial provides a data point that helps to average out random measurement errors.

By conducting several replications, researchers can ensure that any anomalies or outliers in individual trials are balanced by consistent trends seen across experiments. This method also increases the statistical power of the experiment and provides a more reliable estimate of the true effect being studied. Overall, replication is vital for confirming the validity and accuracy of the experimental findings.
Reducing Variability
Reducing variability in experimental results is essential for achieving consistent and reliable data. One effective way to minimize variability is through increased replications. The more you replicate an experiment, the more random errors cancel out, leading to measurements that are closer to the true value.

Another strategy is to standardize procedures as much as possible. This includes using precise measuring instruments and ensuring that all conditions, like temperature and humidity, remain constant throughout the experiment. Implementing these strategies helps in reducing the variability and improving the overall quality and confidence in the experimental results.
Experimental Precision
Experimental precision refers to the consistency and repeatability of measurements within an experiment. It's a measure of how close repeated measurements are to each other. Precision is crucial in experiments as it reflects the reliability of the measurements. Anything that helps to reduce variability tends to improve precision.

To enhance precision, researchers often use standardized methods and well-calibrated equipment. High precision implies that there is less spread in the measurements, indicating that the results are reliable. It's important to note that precision is different from accuracy, which refers to how close the measurements are to the true value, but both are essential for high-quality scientific research.

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

A paper manufacturer requires a minimum strength of 20 pounds per square inch. To check on the quality of the paper, a random sample of 10 pieces of paper is selected each hour from the previous hour's production and a strength measurement is recorded for each. Assume that the strength measurements are normally distributed with a standard deviation \(\sigma=2\) pounds per square inch. a. What is the approximate sampling distribution of the sample mean of \(n=10\) test pieces of paper? b. If the mean of the population of strength measurements is 21 pounds per square inch, what is the approximate probability that, for a random sample of \(n=10\) test pieces of paper, \(\bar{x}<20 ?\) c. What value would you select for the mean paper strength \(\mu\) in order that \(P(\bar{x}<20)\) be equal to \(.001 ?\)

The normal daily human potassium requirement is in the range of 2000 to 6000 milligrams (mg), with larger amounts required during hot summer weather. The amount of potassium in food varies, but bananas are often associated with high potassium, with approximately \(422 \mathrm{mg}\) in a medium sized banana \(^{8}\). Suppose the distribution of potassium in a banana is normally distributed, with mean equal to \(422 \mathrm{mg}\) and standard deviation equal to \(13 \mathrm{mg}\) per banana. You eat \(n=3\) bananas per day, and \(T\) is the total number of milligrams of potassium you receive from them. a. Find the mean and standard deviation of \(T\). b. Find the probability that your total daily intake of potassium from the three bananas will exceed \(1300 \mathrm{mg} .\) (HINT: Note that \(T\) is the sum of three random variables, \(x_{1}, x_{2},\) and \(x_{3},\) where \(x_{1}\) is the amount of potassium in banana number \(1,\) etc. \()\)

The battle for consumer preference continues between Pepsi and Coke. How can you make your preferences known? There is a web page where you can vote for one of these colas if you click on the link that says PAY CASH for your opinion. Explain why the respondents do not represent a random sample of the opinions of purchasers or drinkers of these drinks. Explain the types of distortions that could creep into an Internet opinion poll.

Contrary to current thought about omega- 3 fatty acids, new research shows that the beneficial fats may not help reduce second heart attacks in heart attack survivors. The study included 4837 men and women being treated for heart disease. The experimental group received an additional \(400 \mathrm{mg}\) of the fats daily. \({ }^{1}\) Suppose that this experiment was repeated with 50 individuals in the control group and 50 individuals in the experimental group. Determine a randomization scheme to assign the 100 individuals to the two groups.

Recycling trash, reducing waste, and reusing materials are eco-actions that will help the environment. According to a USA Today snapshot (Exercise 6.45), \(78 \%\) of respondents list recycling as the leading way to help our environment. \({ }^{11}\) Suppose that a random sample of \(n=100\) adults is selected and that the \(78 \%\) figure is correct. a. Does the distribution of \(\hat{p},\) the sample proportion of adults who list recycling as the leading way to help the environment have an approximate normal distribution? If so, what is its mean and standard deviation? b. What is the probability that the sample proportion \(\hat{p}\) is less than \(75 \% ?\) c. What is the probability that \(\hat{p}\) lies in the interval .7 to .75? d. What might you conclude about \(p\) if the sample proportion were less than \(.65 ?\)

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.