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Chapter 7: Problem 69

A biology experiment was designed to determine whether sprouting radish seeds inhibit the germination of lettuce seeds. \({ }^{18}\) Three 10-centimeter petri dishes were used. The first contained 26 lettuce seeds, the second contained 26 radish seeds, and the third contained 13 lettuce seeds and 13 radish seeds. a. Assume that the experimenter had a package of 50 radish seeds and another of 50 lettuce seeds. Devise a plan for randomly assigning the radish and lettuce seeds to the three treatment groups. b. What assumptions must the experimenter make about the packages of 50 seeds in order to assure randomness in the experiment?

Short Answer

Expert verified
Answer: The key steps in randomly assigning seeds to the treatment groups are: 1. Ensure equal chance of each seed being selected for the experiment by mixing them thoroughly. 2. Randomly assign 26 lettuce seeds to the first petri dish, and 13 lettuce seeds to the third petri dish. The remaining 11 lettuce seeds will not be used. 3. Randomly assign 26 radish seeds to the second petri dish, and 13 radish seeds to the third petri dish. The remaining 11 radish seeds will not be used. The assumptions made to assure randomness in the experiment are: 1. Both packages of seeds are well-mixed, with no clustering of seeds in any part of the package. 2. Each seed in the packages has an equal chance of being chosen during the seed selection process, which can be carried out using a random selection approach such as numbering each seed and using a random number generator to select the seeds.

Step by step solution

01

Ensure equal chance of each seed being selected

To make sure the experiment is random, each seed should have an equal chance of being selected for each group. This can be done by mixing the seeds thoroughly and then randomly selecting them.
02

Assign lettuce seeds to the groups

Start by randomly assigning lettuce seeds to the groups: 1. Randomly select 26 lettuce seeds and place them in the first petri dish 2. Randomly select 13 lettuce seeds and place them in the third petri dish The remaining 11 lettuce seeds in the package will not be used in this experiment.
03

Assign radish seeds to the groups

Next, randomly assign radish seeds to the groups: 1. Randomly select 26 radish seeds and place them in the second petri dish 2. Randomly select 13 radish seeds and place them in the third petri dish The remaining 11 radish seeds in the package will not be used in this experiment.
04

Assumptions to assure randomness

The experimenter must make the following assumptions to assure randomness in the experiment: 1. Both packages of seeds are well-mixed, meaning there is no clustering of seeds in any part of the package. 2. Each seed in the packages has an equal chance of being chosen during the seed selection process. This can be done by using any random selection approach. One method could be numbering each seed and using a random number generator to select the seeds.

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Key Concepts

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

Random Assignment
In experimental design, Random Assignment is crucial. It helps ensure that each seed has an equal opportunity to be placed in any group. By doing this, influences outside of the variables being tested are minimized, enabling a fair analysis of the results. To achieve random assignment in an experiment, the seeds can be thoroughly mixed before selection. This randomization is fundamental in creating unbiased results. Random assignment allows researchers to confidently attribute differences in outcomes to the experiment itself, rather than to pre-existing variances among the seeds.
Control Group
A Control Group in an experiment serves as a baseline for comparison. It helps in understanding the effect of the experiment by providing a point of reference that has not been affected by the variable being tested. In the context of our seed experiment, an ideal control group might be the petri dish containing only lettuce seeds. By not mixing with radish seeds, this control group allows researchers to observe how lettuce seeds germinate without any interference. The data from the control group can then be compared to those from treatment groups to assess the true effect of the radish seeds.
Biased Sample
A Biased Sample occurs when some members of the population have a different probability of being included in the sample regularly. In experimentation, a biased sample can skew results, leading to incorrect conclusions. It's crucial to ensure that samples represent the whole population as closely as possible. For instance, if the lettuce or radish seeds were clustered together, or if the same group of seeds was repeatedly selected, this could introduce bias. To avoid this, each seed should have an equal chance of selection, which can be accomplished by mixing seeds thoroughly or using a random selection method. 假如某种偏差存在，那么实验结果可能极为不可靠。避免这种情况非常重要。
Treatment Groups
Treatment Groups in an experiment receive the specific conditions being tested. These groups are compared to the control group to understand the effects of the experiment. In our radish and lettuce seed experiment, there are two treatment groups:
  • The third petri dish containing both 13 lettuce and 13 radish seeds.
This setup allows researchers to observe how the presence of radish seeds affects the germination of lettuce seeds. By comparing the treatment groups to the control group (only lettuce seeds), researchers can determine the influence of radish seeds on lettuce seed germination.

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Most popular questions from this chapter

The sample means were calculated for 30 samples of size \(n=10\) for a process that was judged to be in control. The means of the \(30 \bar{x}\) -values and the standard deviation of the combined 300 measurements were \(\overline{\bar{x}}=20.74\) and \(s=.87,\) respectively. a. Use the data to determine the upper and lower control limits for an \(\bar{x}\) chart. b. What is the purpose of an \(\bar{x}\) chart? c. Construct an \(\bar{x}\) chart for the process and explain how it can be used.

Black Jack A gambling casino records and plots the mean daily gain or loss from five blackjack tables on an \(\bar{x}\) chart. The overall mean of the sample means and the standard deviation of the combined data over 40 weeks were \(\overline{\bar{x}}=\$ 10,752\) and \(s=\$ 1605\), respectively. a. Construct an \(\bar{x}\) chart for the mean daily gain per blackjack table. b. How can this \(\bar{x}\) chart be of value to the manager of the casino?

Suppose a telephone company executive wishes to select a random sample of \(n=20\) out of 7000 customers for a survey of customer attitudes concerning service. If the customers are numbered for identification purposes, indicate the customers whom you will include in your sample. Use the random number table and explain how you selected your sample.

Explain the difference between an \(\bar{x}\) chart and a \(p\) chart.

A hardwoods manufacturing plant has a production line designed to produce baseball bats weighing 32 ounces. During a period of time when the production process was known to be in statistical control, the average bat weight was found to be 31.7 ounces. The observed data were gathered from 50 samples, each consisting of 5 measurements. The standard deviation of all samples was found to be \(s=.2064\) ounces. Construct an \(\bar{x}\) -chart to monitor the 32 -ounce bat production process.
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