Having done poorly on a particular exam in a junior high school, 24 students decide to write the exam again to try and improve their mark. Results are given in the following table. Student Attempt 1 (A1) Attempt 2 (A2) Difference (d- A1 - A2) Average Standard deviation 24 55 3.0 24 58 4.4 24 -3.0 2.4 (a) Find an 80% confidence interval for the difference in mean scores between attempt 1 and attempt 2. (Round your answers to 4 decimal places, if needed.) (b) Based on this confidence interval, can we conclude there is a difference in mean scores between attempt 1 and attempt 2? O Yes, since the interval is completely below 0. O No, since the interval contains 0. O Yes, since the interval contains 0.
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.
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