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Chapter 3: Problem 22

The data in the next column represent the number of pods on a sample of soybean plants for two different plot types. Which plot type do you think is superior? Why? $$ \begin{array}{llllllllll} \text { Plot Type } & \multicolumn{7}{c} {\text { Pods }} \\ \hline \text { Liberty } & 32 & 31 & 36 & 35 & 44 & 31 & 39 & 37 & 38 \\ \hline \text { No Till } & 35 & 31 & 32 & 30 & 43 & 33 & 37 & 42 & 40 \end{array} $$

Short Answer

Expert verified
No Till plot type is superior because it has a higher mean number of pods.

Step by step solution

01

Calculate the Mean for Each Plot Type

Calculate the average number of pods for each plot type to find which one has a higher mean. The formula for the mean is \(\bar{x} = \frac{\text{sum of all data points}}{\text{number of data points}}\).
02

Mean Calculation for Liberty Plot

Sum the number of pods for the Liberty plot type and divide by the total number of data points. \(\bar{x}_{\text{Liberty}} = \frac{32 + 31 + 36 + 35 + 44 + 31 + 39 + 37 + 38}{9} = 36\).
03

Mean Calculation for No Till Plot

Sum the number of pods for the No Till plot type and divide by the total number of data points. \(\bar{x}_{\text{No Till}} = \frac{35 + 31 + 32 + 30 + 43 + 33 + 37 + 42 + 40}{9} 鈮� 36.11\).
04

Compare the Means

Compare the calculated means. The plot type with the higher mean is considered superior in terms of the number of pods. Liberty has a mean of 36, while No Till has a mean of approximately 36.11.
05

Conclusion

Based on the mean calculations, No Till plot type has a slightly higher mean number of pods compared to the Liberty plot type.

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Key Concepts

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

descriptive statistics
Descriptive statistics involves summarizing and interpreting data in meaningful ways. This helps us understand the main features of a dataset quickly. In this exercise, we calculated the mean for the number of pods in different plot types. The mean, a measure of central tendency, gives an average value and helps compare groups. It's essential for understanding the overall spread and tendencies in our data.
data analysis
Data analysis is about understanding and interpreting data to make informed decisions. By calculating the mean number of pods for each plot type, we analyzed how different environments affect soybean growth. This analysis involves:
  • Gathering data
  • Performing calculations
  • Interpreting results
These steps help us determine which plot type performs better, providing insights based on empirical evidence.
mean comparison
Comparing means is vital in identifying differences between groups. In this problem, we compared the average number of pods between Liberty and No Till plot types. By doing this, we aimed to find which plot type yields more pods overall. The No Till plot type showed a slightly higher mean (36.11) compared to Liberty (36). Even small differences in means can indicate significant insights into agricultural practices.
sample data
Sample data refers to a subset selected from a larger population for analysis. Here, the number of pods from a sample of soybean plants in different plots was used. Using sample data is practical because it鈥檚 often impossible to gather data from an entire population. This sample data helps us make estimations about the general performance of the plot types.
experimental plots
Experimental plots are specific areas where different conditions are applied to study their effects. In this exercise, Liberty and No Till are the two plot types being compared. By evaluating the number of pods in these plots, we can understand how different treatments affect soybean plant growth. Experimental plots are crucial for testing hypotheses and improving agricultural methodologies.

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Most popular questions from this chapter

Lawrence Summers (former Secretary of the Treasury and former president of Harvard) infamously claimed that women have a lower standard deviation IQ than men. He went on to suggest that this was a potential explanation as to why there are fewer women in top math and science positions. Suppose an IQ of 145 or higher is required to be a researcher at a top-notch research institution. Use the idea of standard deviation, the Empirical Rule, and the fact that the mean and standard deviation IQ of humans is 100 and 15 , respectively, to explain Summers' argument.

Find the population variance and standard deviation or the sample variance and standard deviation as indicated. $$ \text { Population: } 4,10,12,12,13,21 $$

Babies born after a gestation period of 32-35 weeks have a mean weight of 2600 grams and a standard deviation of 660 grams. Babies born after a gestation period of 40 weeks have a mean weight of 3500 grams and a standard deviation of 470 grams. Suppose a 34 -week gestation period baby weighs 2400 grams and a 40 -week gestation period baby weighs 3300 grams. What is the \(z\) -score for the 34 -week gestation period baby? What is the \(z\) -score for the 40 -week gestation period baby? Which baby weighs less relative to the gestation period?

A certain type of concrete mix is designed to withstand 3000 pounds per square inch (psi) of pressure. The strength of concrete is measured by pouring the mix into casting cylinders after it is allowed to set up for 28 days. The following data represent the strength of nine randomly selected casts. Compute the range and sample standard deviation for the strength of the concrete (in psi). $$ 3960,4090,3200,3100,2940,3830,4090,4040,3780 $$

The following data represent the diagnosis of a random sample of 20 patients admitted to a hospital. Determine the mode diagnosis. $$ \begin{array}{lll} \hline \text { Cancer } & \begin{array}{l} \text { Motor vehicle } \\ \text { accident } \end{array} & \begin{array}{l} \text { Congestive heart } \\ \text { failure } \end{array} \\ \hline \text { Gunshot wound } & \text { Fall } & \text { Gunshot wound } \\ \hline \text { Gunshot wound } & \begin{array}{l} \text { Motor vehicle } \\ \text { accident } \end{array} & \text { Gunshot wound } \\ \hline \text { Assault } & \begin{array}{l} \text { Motor vehicle } \\ \text { accident } \end{array} & \text { Gunshot wound } \\ \hline \begin{array}{l} \text { Motor vehicle } \\ \text { accident } \end{array} & \begin{array}{l} \text { Motor vehicle } \\ \text { accident } \end{array} & \text { Gunshot wound } \\ \hline \begin{array}{l} \text { Motor vehicle } \\ \text { accident } \end{array} & \text { Gunshot wound } \\ \hline \text { Fall } & \begin{array}{l} \text { Motor vehicle } \\ \text { accident } \end{array} \\ \hline \text { Source: Tamela Ohm, student at Joliet Junior College } \end{array} $$
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