Question

g and h are for problem #1

Problem Set Chapters 10 & 12 [44 MARKS] Please print out and complete this problem set on your own and bring it to the next exam to be handed in at the start of the final exam. Be sure to show your calculations. Attach a separate piece of paper if needed Medical researchers have explored the use of deep brain electrical stimulation to control intractable epilepsy not adequately controlled by medication. A researcher interested in spatial navigation recruited 18 patients receiving deep-brain stimulation of the hippocampus to control their seizures and asked them to learn to navigate through a maze. Nine of the participants were given absolute directions (e.g., "walk straight for 20 paces and take the left turn") and the other nine participants were given landmark-based directions (e.g., "walk until you reach the turn across from the statue"). The researcher hypothesized that stimulation of the hippocampus would benefit landmark learning, and so the group receiving landmark instructions would make fewer errors. The researcher records the number of errors made by each participant. A summary of these data appears below 1. Landmark Absolute 9 45 54 2X Compute the Mean number of errors made by participants for each of the two experimental groups [2 marks a. State the null hypothesis, Ho, and the alternative hypothesis, Ha, that reflect the researcher's hypothesis described above [2 marks] b. c. What is the degrees of freedom for this hypothesis test? [1 mark] d. Assuming a Type I error rate a 0.05, what is teritical for this experiment? [1 mark] e. Compute SS for each of the two experimental groups [2 marks] f. Compute SM-M2 (round to 3 decimal places) [3 marks] e Computethe t static for these data [2 marks] Based on your t statistic, what would the researcher conclude about whether deep- brain stimulation is more beneficial for remembering landmark-based directions? [1 mark) h.

Answer 1

(e) the t-statistic is =10.0275

(f) yes, deep brain stimulation is more beneficial

as the one-tailed p-value is less than the typical level of significance alpha=0.05, so we reject null hypothesis and concolcude that  deep brain stimulation is more beneficial

following information has been generated using ms-excel

n	9	9
sum(x)	45	54
sum(x2)	249	358
sum((x-mean(x))2)	24	34

sum((x-mean(x))²)=sum(x²)-sum(x)*sum(x)/n

here we use t-test with

null hypothesis H0:mean1=mean2 and alternate hypothesis H1:mean1< mean2 ( this is left-one-tailed test)

statistic t=|(mean1-mean2)|/((s_p*(1/n1 +1/n2)^1/2) with df is n=n1+n2-2 and s_p²=((n1-1)s1²+(n2-1)s2²)/n

t-test
	sample	mean			n	(n-1)s2
	landmark	45.0000			9	24.0000
	absolute	54.0000			9	34.0000
	difference=	9.0000			18	58.0000
	sp2=	3.6250
	sp=	1.9039
	SE=	0.8975
	t=	10.0275
one tailed	p-value=	0.0000
two tailed	p-value=	0.0000
two tialed critical	t(0.05)	2.1199
one tailed critical	t(0.05)	1.7459