Question

Help. Please show work.

Hypo 2 5. In a study to investigate the effect of ultrasound therapy on kne etension, range of motion was measured for people in a Name: representative sample of physical therapy patients both before and after ultrasound therapy. Is there evidence that the ultrasound therapy increases range of motion? If independent label what Ai and u are. If these are dependent tell me how you are subtracting them second sample is what? Denend evt Step 1: State the hypothesis, and identify the claim. Step 2: Compute the test value and find p-value. If you answered independent this is a two-part solution and Make sure you indicate if your variances are equal or not. Make the decision to reject or not reject the null hypothesis. Step 3: Compare p-value to alpha. Step 4: Summarize the results. State your conclusion clearly 0543249 3545553 5022941 2545443 1234567

Answer 1

Here first sample is sample of before ultra sound therapy and second sample is sample of after ultra sound therapy.

Here data is collected before and after ultrasound therapy. So this data is dependent data.

d = sample 2 - sample 1

Claim : If ultra sound therapy increases range of motion.

Step 1. The hypothesis are:

H0 : $\mu _{d}$ = 0 v/s H1: $\mu _{d}$ > 0

Step 2. The test statistic is,

$t=\frac{\overline{d}}{s_{d}/\sqrt{n}}$

Before	After	d=After-Before
25	30	5
50	55	5
42	44	2
52	53	1
49	52	3
44	54	10
31	39	8

So here n= 7, $\overline{d}$ = 4.86, s_d = 3.237

4.86 3.237 VT

= 3.972

df = n-1 = 7-1 =6

p value = p ( t > 3.972 ) = 0.0037

( using excel formula "=t.dist.rt(3.972,6)" )

step 3 :

Here p value < $\alpha$ (0.05). Hence we reject null hypothesis

step 4 :

Conclusion : There is sufficient evidence to conclude that ultra sound therapy increases range of motion.