Question

Question 4 options:

To determine if Reiki is an effective method for treating pain, a pilot study was carried out where a certified second-degree Reiki therapist provided treatment on volunteers. Pain was measured using a visual analogue scale (VAS) immediately before and after the Reiki treatment (Olson & Hanson, 1997). The data is in is in following table:

Table: Pain Measures Before and After Reiki Treatment

VAS before	VAS after
6	3
2	1
2	0
9	1
3	0
3	2
4	1
5	2
2	2
3	0
5	1
1	0
6	4
6	1
4	4
4	1
7	6
2	1
4	3
8	8

Does the data show that Reiki treatment reduces pain? Test at the 5% level.

(i) Let μ₁= mean VAS before Reiki treatment. Let μ₂ = mean VAS after Reiki treatment. Which of the following statements correctly defines the null hypothesis H_O?

A. μ₁ − μ₂ > 0 (μ_d> 0)

B. μ₁ – μ₂< 0 (μ_d< 0)

C. μ₁ – μ₂ = 0 (μ_d= 0)

D. μ₁ + μ₂= 0

Enter letter corresponding to correct answer

(ii)   Let μ₁= mean VAS before Reiki treatment. Let μ₂ = mean VAS after Reiki treatment. Which of the following statements correctly defines the null hypothesis H_O?

A. μ₁ − μ₂ < 0 (μ_d< 0)

B. μ₁ – μ₂> 0 (μ_d> 0)

C. μ₁ – μ₂ = 0 (μ_d= 0)

D. μ₁ + μ₂= 0

Enter letter corresponding to correct answer

(iii) Enter the level of significance α used for this test:

Enter in decimal form. Examples of correctly entered answers: 0.01    0.02    0.05    0.10

(iv)  Determine sample mean of differences  x¯d

Enter in decimal form to nearest hundredth (no spaces) Examples of correctly entered answers:

0.01 3.37 -11.47    21.00

(v) Determine sample standard deviation of differences s_d

Enter in decimal form to nearest ten-thousandth. Examples of correctly entered answers:

0.0001    0.0200     3.5607      -0.0074

(vi) Calculate and enter test statistic

Enter value in decimal form rounded to nearest ten-thousandth, with appropriate sign (no spaces). Examples of correctly entered answers:

–2.0104      –0.3070        +1.6000        +11.0019

(vii) Determine degrees of freedom for the sample of differences df_d:

Enter value in integer form. Examples of correctly entered answers:

2    5    9    23    77

(viii) Using tables, calculator, or spreadsheet: Determine and enter p-value corresponding to test statistic.

Enter value in decimal form rounded to nearest ten-thousandth. Examples of correctly entered answers:

0.0001     0.0021     0.0305     0.6004      0.8143    1.0000

(ix) Comparing p-value and α value, which is the correct decision to make for this hypothesis test?

A. Accept H_o

B. Fail to reject H_o

C. Reject H_o

D. Accept H_A

Enter letter corresponding to correct answer.

(x) Select the statement that most correctly interprets the result of this test:

A. The result is statistically significant at .05 level of significance. Sufficient evidence exists to support the claim that the Reiki treatment reduces pain.

B. The result is statistically significant at .05 level of significance. There is not enough evidence to support the claim that the Reiki treatment reduces pain.

C. The result is not statistically significant at .05 level of significance. There is not enough evidence to support the claim that the Reiki treatment reduces pain.

D. The result is not statistically significant at .05 level of significance. Sufficient evidence exists to support the claim that the Reiki treatment reduces pain.

Enter letter corresponding to most correct answer

Answer 1

(i)

Which of the following statements correctly defines the null hypothesis H_O?

Correct option:

C. μ₁ – μ₂ = 0 (μ_d= 0)

(ii)

Which of the following statements correctly defines the alternative hypothesis H_A?

Correct option:

B. μ₁ – μ₂> 0 (μ_d> 0)

(iii)

0.05

(iv)

2.25

Explanation:

From the given data, values of d = VAS before - VAS after are got as follows:

d = VAS before - VAS after = 3,1,2,8,3,1,3,3,0,3,4,1,2,5,0,3,1,1,1,0

From d values, we get:

= Mean of d values = 2.25

(v)

1.943

Explanation:

From d values, we get:

s_d = Standard Deviation of d values = 1.9433

(vi)

5.1779

Explanation:

Test Statistic is given by:

(vii)

19

(viii)

0.0000

(ix)

C

Explanation:

C. Reject H_o

(x)

A

Explanation:

A. The result is statistically significant at .05 level of significance. Sufficient evidence exists to support the claim that the Reiki treatment reduces pain.