esearcher wanted to determine if the mean time to complete a bachelor’s degree was different depending on the selectivity of the first institution of higher education that was attended. The following data represent a random sample of 12th-graders in 1992 who earned their degree by December 2000. Highly Selective Selective Nonselective Open-door Not Rated 2.6 3.1 4.7 5 4.5 4.1 3.8 4.2 7.3 5.5 3.4 5.2 5.7 5.6 5.5 4.3 4.5 2.3 6.9 4.6 3.9 4 4.5 5.1 4.1 2.5 4.6 4.7 5.9 5.1 5.1 4.3 2.3 4.2 4.3 4.3 4.4 4.3 6.4 4.4 4.8 4 4.2 5.6 3.8 5.5 4.1 5.1 6 4.7 1) What is your decision about the null hypothesis, consider ?. 2) If your decision in part (4) was reject , perform Tukey test to determine which pairwise means are significantly different using a familywise error rate of : 5.a) How many pairwise comparisons are possible among the treatment levels?. 5.b) Compute and .
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.
researcher wanted to determine if the mean time to complete a bachelor’s degree was different depending on the selectivity of the first institution of higher education that was attended. The following data represent a random sample of 12th-graders in 1992 who earned their degree by December 2000.
Highly Selective | Selective | Nonselective | Open-door | Not Rated |
2.6 | 3.1 | 4.7 | 5 | 4.5 |
4.1 | 3.8 | 4.2 | 7.3 | 5.5 |
3.4 | 5.2 | 5.7 | 5.6 | 5.5 |
4.3 | 4.5 | 2.3 | 6.9 | 4.6 |
3.9 | 4 | 4.5 | 5.1 | 4.1 |
2.5 | 4.6 | 4.7 | 5.9 | 5.1 |
5.1 | 4.3 | 2.3 | 4.2 | 4.3 |
4.3 | 4.4 | 4.3 | 6.4 | 4.4 |
4.8 | 4 | 4.2 | 5.6 | 3.8 |
5.5 | 4.1 | 5.1 | 6 | 4.7 |
1) What is your decision about the null hypothesis, consider ?.
2) If your decision in part (4) was reject , perform Tukey test to determine which pairwise means are significantly different using a familywise error rate of :
5.a) How many pairwise comparisons are possible among the treatment levels?.
5.b) Compute and .
5.c) Compute the test statistic, , for each pairwise comparison.
5.d) Write the null hypothesis and the alternative hypothesis for each pairwise comparison.
5.e) What is your decision about the null hypotheses, Explain your answers
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