25 25 27 32 Treatments B 17 19 25 18 17 22 26 26 30 27 18 XA = 25.4 SÅ = 25.3 = 19.2 = 26.2 %3D XB SB = 11.2 SC = 8.2 %3D
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
A random sample of five observations from three
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a. Calculate the grand mean. (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)
b. Calculate SSTR and MSTR. (Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)
c. Calculate SSE and MSE. (Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)
d. Specify the competing hypotheses in order to determine whether some differences exist between the population means.
_H0: μA = μB = μC; HA: Not all population means are equal.
_H0: μA ≤ μB ≤ μC; HA: Not all population means are equal.
_H0: μA ≥ μB ≥ μC; HA: Not all population means are equal.
e-1. Calculate the value of the F(df1, df2) test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)
e-2. Find the p-value.
_0.025 p-value < 0.05
_0.01 p-value < 0.025
_p-value < 0.01
_p-value 0.10
_0.05 p-value < 0.10
f. At the 10% significance level, what is the conclusion to the test?
_Reject H0 since the p-value is less than significance level.
_Do not reject H0 since the p-value is not less than significance level.
_Do not reject H0 since the p-value is less than significance level.
_Reject H0 since the p-value is not less than significance level.
g. Interpret the results at αα = 0.10.
_We cannot conclude that some means differ.
_We conclude that some means differ.
_We conclude that all means differ.
_We conclude that population mean C is greater than population mean A.
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