Question

A project based on touch therapy is presented at a science fair by a local high school student. In the study, practitioners of touch therapy are blindfolded to see if they can detect a "human energy field (HEF)" without touching patients. The student believes that a practitioner with less years of experience predicts more correct choices to detect HEF. What can be concluded with α = 0.01?

experience	HEF
22 21 12 15 9 28 7 15 13 9	2 4 5 5 3 1 7 3 4 4

a) What is the appropriate statistic?
---Select--- na Correlation Slope Chi-Square
Compute the statistic selected above:  

b) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
Critical value =  ; Test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

c) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
Effect size =  ;   ---Select--- na trivial effect small effect medium effect large effect

d) Make an interpretation based on the results.

Practitioners with more years of experience predict more HEF correctly.Practitioners with less years of experience predict more HEF correctly.    Practitioners' years of experience does not predict detecting HEF.

Answer 1

(first) correlation

Correlation coefficient indicates the extent to which two or more variables fluctuate together. A positive correlation indicates the extent to which those variables increase or decrease in parallel; a negative correlation indicates the extent to which one variable increases as the other decreases.

(second) here the null hypothesis H0:=0 and alternate hypothesis Ha:<0

we use t-test and statistic t=r/sqrt((1—r²)/(n—2))==(-0.7267)/SQRT((1-(-0.7267)*(-0.7267))/(10-2))=-2.99

the correlation coefficient =r=-0.7267

The one tailed critical t(0.05,8)=1.86 is less than absolute value calcuated t=2.99, so we reject the null hypothesis and conclude that correlation is less than 0 or negative

(third) effect size=r²=(-0.7267)*(-0.726

(fourth) Practitioners with less years of experience predict more HEF correctly.

since the there is negative correlation between (Practitioners with less years of experience) and( prediction of HEF correctly.)