The local school board has instituted a book rewards program intended to encourage third graders to read more, thereby increasing their scores on a standardized vocabulary test. Nationally, the average score on this exam among third graders is 98. A random sample of 223 local third graders participating in the program scored an average of 104 on the test with a standard deviation of 13. Conduct a significance test with a=.05 to answer the research question: Is the program working to significantly increase local third graders' vocabulary scores? What is the probability that your obtained score is wrong, assuming the null hypothesis is true? Do you reject the null or fail to reject the null based on the program working?
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.
- The local school board has instituted a book rewards program intended to encourage third graders to read more, thereby increasing their scores on a standardized vocabulary test. Nationally, the average score on this exam among third graders is 98. A random sample of 223 local third graders participating in the program scored an average of 104 on the test with a standard deviation of 13. Conduct a significance test with a=.05 to answer the research question: Is the program working to significantly increase local third graders' vocabulary scores?
- What is the probability that your obtained score is wrong, assuming the null hypothesis is true?
- Do you reject the null or fail to reject the null based on the program working?
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