The average final exam score for the statistics course is 77% and the standard deviation is 8%. A professor wants to see if there will be a difference in the average final exam score for students who are given colored pens on the first day of class. The final exam scores for the 18 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal. 75, 88, 84, 68, 96, 72, 81, 97, 77, 79, 85, 81, 52, 80, 98, 83, 78, 90 What can be concluded at the 0.05 level of significance? H0: = 77 Ha: [ Select ] ["<", "Not Equal To", ">"] 77 Test statistic: [ Select ] ["Z", "T"] p-Value = [ Select ] ["0.16", "0.01", "0.08", "0.02"] [ Select ] ["Fail to Reject Ho", "Reject Ho"] Conclusion: There is [ Select ] ["insufficient", "statistically significant"] evidence to make the conclusion that the population mean final exam score for students who are given colored pens at the beginning of class is not equal to 77%.
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 average final exam score for the statistics course is 77% and the standard deviation is 8%. A professor wants to see if there will be a difference in the average final exam score for students who are given colored pens on the first day of class. The final exam scores for the 18 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal.
75, 88, 84, 68, 96, 72, 81, 97, 77, 79, 85, 81, 52, 80, 98, 83, 78, 90
What can be concluded at the 0.05 level of significance?
H0: = 77
Ha: [ Select ] ["<", "Not Equal To", ">"] 77
Test statistic: [ Select ] ["Z", "T"]
p-Value = [ Select ] ["0.16", "0.01", "0.08", "0.02"]
[ Select ] ["Fail to Reject Ho", "Reject Ho"]
Conclusion: There is [ Select ] ["insufficient", "statistically significant"] evidence to make the conclusion that the population
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