31 36 39 35 31 32 24 27 28 28 30 31 . What is the value of the Test Statistic? -. What is the p-value? . State your conclusion. (Hint: Do you reject or not reject Ho at the 5% level).
31 36 39 35 31 32 24 27 28 28 30 31 . What is the value of the Test Statistic? -. What is the p-value? . State your conclusion. (Hint: Do you reject or not reject Ho at the 5% level).
31 36 39 35 31 32 24 27 28 28 30 31 . What is the value of the Test Statistic? -. What is the p-value? . State your conclusion. (Hint: Do you reject or not reject Ho at the 5% level).
To study the effect of temperature on yield in a chemical process, five batches were produced at each of three temperature levels. The results are attached as an Excel file. Using Excel, construct an analysis of variance table. Use a .05 level of significance to test whether the temperature level has an effect on the mean yield of the process.
Transcribed Image Text:### Data Set
The image presents a dataset organized in three columns with five numerical entries each. The columns are not labeled, but the numbers suggest different sets or groups:
- **Column 1**: 31, 36, 39, 35
- **Column 2**: 31, 32, 24, 27
- **Column 3**: 28, 28, 30, 31
### Questions
a. **What is the value of the Test Statistic?**
b. **What is the p-value?**
c. **State your conclusion. (Hint: Do you reject or not reject Ho at the 5% level).**
### Explanation
This exercise seems to be related to hypothesis testing, likely requiring the calculation of a test statistic for comparing means across groups. It asks for the following:
1. **Test Statistic**: Calculate the test statistic based on the dataset.
2. **p-value**: Determine the p-value to assess the significance.
3. **Conclusion**: Based on the p-value, decide whether to reject the null hypothesis (Ho) at the 5% level of significance.
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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