Please give answer to question g. We conduct an experiment to determine whether
ID: 3128947 • Letter: P
Question
Please give answer to question g.
We conduct an experiment to determine whether right-handed people react more quickly with their right hand than they do with their left hand. A machine emits a beeping sound and a subject presses a button as quickly as they can once they hear the beep. The right hand and left hand reaction times (in milliseconds) for a sample of seven subjects, along with some summary statistics that may be helpful, are shown below:
(a) Which of the following statements are true?
(I) In order to conduct our inference procedures, we must assume that right hand reaction times and left hand reaction times follow normal distributions.
(II) In order to conduct our inference procedures, we must assume that differences in right and left hand reaction times follow a normal distribution.
(III) For any subject, right hand reaction time and left hand reaction time are independent.
(IV) For any subject, right hand reaction time and left hand reaction time are dependent.
(V) For any two subjects, right hand reaction times are independent.
(b) Calculate a 99% confidence interval for the true mean difference in right hand and left hand reaction times.
(c) We would like to conduct a hypothesis test at the 1% level of significance to determine whether there is evidence that right-handed people react more quickly on average with their right hand than with their left hand. What are the hypotheses for the appropriate test of significance?
(d) What is the value of the test statistic for the appropriate test of significance?
(e) What is the P-value of the test?
(f) What is the appropriate conclusion of the test?
(g) Suppose we had instead conducted the test using the critical value method. What would be the decision rule and the conclusion?
Explanation / Answer
a. ii. This checks the Nearly normal condition (where, histogram of differences is plotted to check whether it is uniform and symmetric). iii. This checks the Independence assumptions wherefor any sample the left hand and right hand reaction times are independent.
b. The 99% ci is as follows:
dbar +- t*n-1 SE(dbar)=-13.86+-3.143 sd/sqrt n
=-13.86+-3.143 *25.12/sqrt7=-13.86 +-29.84=-43.7 to 15.98
c. H0:mur-mud=0 (reaction time of both right hand and left hand of right handed people is same)
H1:mur-mud<0 (reaction time of right hand is quick compared to left hand of right handed people)
d. t=(dbar-0)/SE(dbar)=(-13.86-0)/9.49=-1.46
e. Using technology, the exact p value is 0.195.
f. The p value is not less than 0.01. Therefore, fail to reject null hypothesis. There i snot sufficient sample evidence to ocnclude that reaction time of right hand i smore quick than left hand for right handed people.
g. At df=6 and alpha =0.01, th et critical is 3.143. The test statistic do not fall in the critical region. Therefore, conclusion is same.