You want to see if the average grade for nontraditional age students is less than the average grade for traditional age students. You believe both populations are normally distributed, but you do not know the standard deviations for either. You obtain the following two samples of data. Non-Traditional Age Students Traditional Age Students 53.9 87 102.9 99.8 44.1 63.9 72.6 87.5 70.2 100.8 88.7 114.4 46.9 54.7 83.4 101.4 38 108.9 53.1 88 29.5 121.5 117.5 74.3 79.8 105.2 86.8 94.1 88.1 92.7 77.3 93.2 44.1 98.4 74.4 114.4 72.6 75.8 29.5 88 42.4 105.8 48.2 108.9 68.7 92.7 90.8 97.4 85.7 97.4 62.5 135.7 Use a significance level of 0.050.05 to answer the following. What is the test statistic for this sample? (Report answer accurate to three decimal places.) t-test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value =
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.
You want to see if the average grade for nontraditional age students is less than the average grade for traditional age students.
You believe both populations are normally distributed, but you do not know the standard deviations for either. You obtain the following two samples of data.
| Non-Traditional Age Students | Traditional Age Students |
|---|---|
| 53.9 | 87 |
| 102.9 | 99.8 |
| 44.1 | 63.9 |
| 72.6 | 87.5 |
| 70.2 | 100.8 |
| 88.7 | 114.4 |
| 46.9 | 54.7 |
| 83.4 | 101.4 |
| 38 | 108.9 |
| 53.1 | 88 |
| 29.5 | 121.5 |
| 117.5 | 74.3 |
| 79.8 | 105.2 |
| 86.8 | 94.1 |
| 88.1 | 92.7 |
| 77.3 | 93.2 |
| 44.1 | 98.4 |
| 74.4 | 114.4 |
| 72.6 | 75.8 |
| 29.5 | 88 |
| 42.4 | 105.8 |
| 48.2 | 108.9 |
| 68.7 | 92.7 |
| 90.8 | 97.4 |
| 85.7 | 97.4 |
| 62.5 | 135.7 |
Use a significance level of 0.050.05 to answer the following.
What is the test statistic for this sample? (Report answer accurate to three decimal places.)
t-test statistic =
What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =
State the hypotheses.
That is, there is no evidence to conclude that average grade for nontraditional age students is less than the average grade for traditional age students.
That is, there is evidence to conclude that average grade for nontraditional age students is less than the average grade for traditional age students.
Step by step
Solved in 2 steps with 4 images
