5) Ultrasound is often used to treat soft tissue injuries of the knee. The range of motion of 7 randomly selected   subjects was measured both before and after the ultrasound treatment was applied.   Subject  1  2  3  4  5  6  7 Pre  treatment 31  53  45  57  50  43  32 Post  treatment 32  59  46  64  49  45  40 Find the difference between the pre-treatment and post-treatment for each subject. [For example, for subject 1,  the difference is 31 – 32 = -1 ]  a) Find the sample mean and standard deviation of the difference, called μd. b) Use the matched pair design to determine whether the mean difference, μd, is less than zero. Use α = .05.  [Note: if μd < 0, then this would imply that the pre-treatment measurement is less than the post-treatment   measurement]

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5) Ultrasound is often used to treat soft tissue injuries of the knee. The range of motion of 7 randomly selected   subjects was measured both before and after the ultrasound treatment was applied.  

Subject 

7

Pre 

treatment

31 

53 

45 

57 

50 

43 

32

Post 

treatment

32 

59 

46 

64 

49 

45 

40



Find the difference between the pre-treatment and post-treatment for each subject. [For example, for subject 1,  the difference is 31 – 32 = -1 ] 

a) Find the sample mean and standard deviation of the difference, called μd.

b) Use the matched pair design to determine whether the mean difference, μd, is less than zero. Use α = .05.  [Note: if μd < 0, then this would imply that the pre-treatment measurement is less than the post-treatment   measurement]

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