Question

Several students were tested for reaction times​ (in thousandths of a​ second) using their right and left hands.​ (Each value is the elapsed time between the release of a strip of paper and the instant that it is caught by the​ subject.) Results from five of the students are included in the graph to the right. Use a 0.10 significance level to test the claim that there is no difference between the reaction times of the right and left hands. LOADING... Click the icon to view the reaction time data table. 150100200 170120220Right HandLeft Hand A scatterplot with a horizontal axis labeled “Right Hand” from 100 to 200 in intervals of 10 and a vertical axis labeled “Left Hand” 120 to 220 in intervals of 10 contains 5 points. The approximate coordinates of the points are as follows: (118, 158); (138, 134); (142, 156); (198, 214); (198, 220). What are the hypotheses for this​ test? Let mu Subscript d be the ▼ mean of the differences difference between the means of the right and left hand reaction times. Upper H 0 ​: mu Subscript d ▼ less than less than or equals equals greater than or equals greater than not equals 0 Upper H 1 ​: mu Subscript d ▼ greater than equals not equals greater than or equals less than or equals less than 0 What is the test​ statistic? tequals nothing ​(Round to three decimal places as​ needed.) Identify the critical​ value(s). Select the correct choice below and fill the answer box within your choice. ​(Round to three decimal places as​ needed.) A. The critical value is tequals nothing . B. The critical values are tequals plus or minusnothing . What is the​ conclusion? There ▼ is not is enough evidence to warrant rejection of the claim that there is ▼ no difference a difference between the reaction times of the right and left hands. Click to select your answer(s).

Answer 1

data

right hand	left Hand
118	158
138	134
142	156
198	214
198	220

scatter plot

left Hand 250 200 150 100 50 0 150 100 200 250 0 50

Excel

data -> data analysis -> t-test paired

t-Test: Paired Two Sample for Means
	left Hand	right hand
Mean	176.4	158.8
Variance	1466.8	1363.2
Observations	5	5
Pearson Correlation	0.911989389
Hypothesized Mean Difference	0
df	4
t Stat	2.485042977
P(T<=t) one-tail	0.033921772
t Critical one-tail	1.533206274
P(T<=t) two-tail	0.067843544
t Critical two-tail	2.131846786

$H_o : \mu_d = 0$

$H_a : \mu_d \neq 0$

t = 2.485

Critical value = +- 2.1318

hence we reject the null hypothesis

there is enough evidence

we conclude that there is significant difference