For a particular group of students it is known from historical data that the mean score on a reading test is 75 , with a known standard deviation of 20 . A new method of instruction has been introduced, and it is believed that this new method will increase the mean test score. An increase of 5 units in mean test score is considered to be the minimal important increase. Researchers will take a sample of n=25students who have been instructed using the new method of instruction and calculate the mean reading test score. They will use a significance level of 5%, and test a one-sided alternative hypothesis that the mean is larger than 75 (HA?:?>75). What is the power to detect an increase of 5 units in mean reading score for this test, based on this sample size? Make sure to show your work, and demonstrate an understanding of the underlying concepts.

For a particular group of students it is known from historical data that the mean score on a reading test is 75, with a known standard deviation of 20. A new method of instruction has been introduced, and it is believed that this new method will increase the mean test score. An increase of 5 units in mean test score is considered to be the minimal important increase. Researchers will take a sample of n = 25 students who have been instructed using the new method of instruction and calculate the mean reading test score. They will use a significance level of 5%, and test a one-sided alternative hypothesis that the mean is larger than 75 (HA : ( > 75). What is the power to detect an increase of 5 units in mean reading score for this test, based on this sample size? Make sure to show your work, and demonstrate an understanding of the underlying concepts