Consider the following data. The summary statistics, histogram, and normal quantile plot were generated by Minitab. 27 27 27 28 28 28 28 28 28 29 29 29 29 29 29 29 29 29 29 30 30 30 30 30 30 30 30 30 30 30 30 31 31 31 31 31 31 31 31 32 32 32 32 33 33 33 33 33 34 34 Use parts A-D for reference for answering E. Only part E needs to be answered, A-D are for reference here. (a) Does the histogram indicate normality for the data distribution? Explain. Yes, we observe a bell-shaped, symmetric distribution. Yes, we observe a uniform, symmetric distribution. No, we observe a uniform, skewed distribution. No, we observe a bell-shaped, skewed distribution.
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.
Consider the following data. The summary statistics, histogram, and normal quantile plot were generated by Minitab.
| 27 | 27 | 27 | 28 | 28 | 28 | 28 | 28 | 28 | 29 |
| 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 29 | 30 |
| 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 |
| 30 | 31 | 31 | 31 | 31 | 31 | 31 | 31 | 31 | 32 |
| 32 | 32 | 32 | 33 | 33 | 33 | 33 | 33 | 34 | 34 |
Use parts A-D for reference for answering E. Only part E needs to be answered, A-D are for reference here.
(a) Does the histogram indicate normality for the data distribution? Explain.
Yes, we observe a bell-shaped, symmetric distribution.
Yes, we observe a uniform, symmetric distribution.
No, we observe a uniform, skewed distribution.
No, we observe a bell-shaped, skewed distribution.
(b) Does the normal quantile plot indicate normality for the data distribution? Explain.
Yes, the points fall approximately on a straight line.
No, the points do not fall on a straight line.
No, the points fall approximately on a straight line.
Yes, the points do not fall on a straight line.
(c) Compute the
Check for outliers.
There are no outliers, but two data points fall exactly on the boundary.
There are two outliers.
There are no outliers.
There is one outlier.
(d) Compute Pearson's index. (Round your answer to three decimal places.)
Does the index value indicate skewness?
(e) Using parts (a) through (d), would you say the data are from a
A. No, the graphs do not support normality, there are no apparent outliers, but there is skewness.
B. Yes, the graphs support normality, there are no apparent outliers, but there is skewness.
C. Yes, the graphs support normality, there are no apparent outliers, and there is no skewness.
D. No, the graphs do not support normality, there is no skewness, but there are apparent outliers.
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