Question

7. A psychologist is interested in determining whether immediate memory capacity is affected by sleep loss. Immediate memory is defined as the amount of material that can be remembered immediately after it has been presented. Twelve students are randomly selected from lower division college courses and randomly assigned to two groups of 6 each. One of the groups is sleep deprived for 24 hours before the material is presented. All subjects in the other group receive the normal amount of sleep (7-8 hours). The material consists of a series of slides, with each slide containing nine numbers. Each slide is presented for a short time interval (50 milliseconds), after which the subject must recall as many numbers as possible. On the following page are the results. The scores represent the percentage correctly recalled. Normal Sleep Group: 68 73 72 65 70 73 Sleep Deprived Group: 70 62 68 63 69 60

a. Describe (1) the independent variable and its levels, and (2) the dependent variable and its scale of measurement. Independent Variable- immediate memory capacity is affect by sleep Dependent- Variable- Scores represent the percentage correctly recalled between two groups b. Describe the null and alternative hypotheses for the study described. c. Using Excel, conduct a statistical test of the null hypothesis at p = .05. Be sure to properly state your statistical conclusion. d. Provide an interpretation of your statistical conclusion in part C. e. What type of statistical error might you have made in part C? f. Obtain the 95% confidence interval using the obtained statistic. g. Provide an interpretation of the confidence interval obtained in part f. h. Does the confidence interval obtained support your statistical conclusion? Explain your answer.

Answer 1

(a1) independent variable: sleep loss , here it has one level.

(a2) dependent variable : immediate memory capacity (which is scores represent the percentage correctly recalled) its scale is ratio

(b)  here we use t-test with

null hypothesis H0:mean1=mean2 and alternate hypothesis H1:mean1≠mean2

(c) statistic t=|(mean1-mean2)|/((s_p*(1/n1 +1/n2)^1/2) =4.8333/2.1461=2.2522 with df is n=n1+n2-2=10

and s_p²=((n1-1)s1²+(n2-1)s2²)/n=13.8167

since two-tailed critical t is less than calculated t, so we reject null hypothesis ( or fail to accept H0)

(d) since we reject H0, it means mean value of normal sleep is greater than deprived sleep and it can be concluded that there is sufficient evidence that  immediate memory capacity is affected by sleep loss.

	sample	mean	s	s2	n	(n-1)s2
	normal	70.1667	3.1885	10.1667	6	50.8333
	deprived	65.3333	4.1793	17.4667	6	87.3333
	difference=	4.8333	sum=	27.6333	12	138.1667
	sp2=	13.8167
	sp=	3.7171
	SE=	2.1461
	t=	2.2522
one tailed	p-value=	0.0240
two tailed	p-value=	0.0480
critical	t(0.05)	2.2281

(e) since we reject H0, so there is chance of type I error

type I error: reject H0 when it is true

Type II error: accept H0 hen it is false

(f) 95% confidence interval of difference of mean=sample mean differencet(0.05/2, df=10)*SE(difference)=

4.83332.2281*2.1461=4.83334.7817=(0.0516, 9.6150)

(g)To interpret a confidence interval the sample information is random - but there is a pattern to its behavior if we look at all possible samples. Each possible sample gives us a different interval. But, even though the results vary from sample-to-sample, we are "confident" because the margin-of-error would be satisfied for 95% of all samples.The margin-of-error being satisfied means that the interval includes the true population value.

(h) yes, confidence interval obtained support your statistical conclusion, as the confidence interval does not include tha 0, so we reject H0.