Do students tend to improve (increase) their math SAT scores the second time they take the test? A random sample of four students who took the test twice received the following scores. Student First Score Second Score Difference 2nd score - 1st score 1 450 440 -10 2 520 600 80 3 720 720 0 4 600 630 30 Mean Standard Deviation 40.41 Assume that the change in math SAT score (second score – first score) for the population of all students taking the test the difference is approximately normally distributed. Calculate the needed statistic to complete the table above in order to perform a hypothesis test. To determine if students tend to improve (increase) their math SAT scores the second time they take the test state the null and alternative hypothesis. Calculate the t statistic. (round to 3 decimal places) How many degrees of freedom? At a level of significance of what is your conclusion
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.
Do students tend to improve (increase) their math SAT scores the second time they take the test? A random sample of four students who took the test twice received the following scores.
|
Student |
First Score |
Second Score |
Difference 2nd score - 1st score |
|
1 |
450 |
440 |
-10 |
|
2 |
520 |
600 |
80 |
|
3 |
720 |
720 |
0 |
|
4 |
600 |
630 |
30 |
|
|
|
|
|
|
Mean |
|
||
|
Standard Deviation |
40.41 |
Assume that the change in math SAT score (second score – first score) for the population of all students taking the test the difference is approximately normally distributed.
Calculate the needed statistic to complete the table above in order to perform a hypothesis test.
To determine if students tend to improve (increase) their math SAT scores the second time they take the test state the null and alternative hypothesis.
Calculate the t statistic. (round to 3 decimal places)
How many degrees of freedom? At a level of significance of what is your conclusion
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