In the Spring semester homework was completed online giving students instant

# In the spring semester homework was completed online

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paper, checking answers in the back of the book. In the Spring semester, homework was completed online – giving students instant feedback on their work. The results are summarized below. Population standard deviations were used from past studies. Online (Group 1) Pen and Paper (Group 2)
Number of Students 144 127 Mean Test Score 78.4 75 Population Standard Dev. Test Score 11.98 10.56 Is there evidence to suggest that the online system improves test scores? Use α=0.05.Select the correct alternative hypothesis and state the p-value.
A physical therapist believes that at 30 years old adults begin to decline in flexibility and agility. To test this, he randomly samples 25 of his patients who are less than 30 years old and 27 of his patients are 30 or older and measures each patient’s flexibility in the Sit-and-Reach test. Assume the populations are normally distributed. The results are below.Less Than 30 (Group 1)30 or Older (Group 2)n2527Mean Sit-and-Reach Score20.2118.99Population Standard Dev. Sit-and-Reach Score2.2222.121Is there evidence to suggest that adults under the age of 30 are more flexible? Round to 4 decimal places. Make sure you put the 0 in front of the decimal.Use α=0.05 .
μ μ μ ≠ μ μ ≤ μ μ ≥ μ μ ≠ μ μ μ μ ≥ μ μ ≤ μ μ μ μ μ μ μ μ μ
β
H 0 H 1 H 0 H 0 H 0