Alice Chen (ac48272) PHY 117M (59065) 2/10/14
Chapter 1: Reactin !i"e !i"e 1# ´ an 'tanar e*iatin ' !a$le !a$le 1: %a"ple Calc&latin' the "ean "ean X Condition Mean (ms) Standard Deviation (ms) A&i Reactin !i"e 152#95 51#81 +i'&al Reactin !i"e 146#71 ,8#50 Ran" +i'&al Reactin ,57#55 60#81 !i"e Mean -
∑ X n
-
148
+ 174 + 162 +117+ … +241 +188 100
∑ ( x − x´ )
2
%tanar .e*iatin 2
n −1 2
2
2
( 148−152.95 ) +(174 −152.95 ) +(162− 152.95) + … +( 188−152.95 ) 99
2# !a$le !a$le 2: re&enc re&enc ta$le ta$le r 100 "ea'&re"ent' "ea'&re"ent' a&i reactin reactin ti"e "ea'&re"ent' "ea'&re"ent' n the $rer are 3r&pe int the hi3her inter*al (e#3# 100 i' 3r&pe in the 100150 inter*al) nter*al !all re&enc 1050 4 5090 1 901,0 2, 1,0170 49 170210 1, 210250 5 250290 , 290,,0 1 ,,0,70 ,70410 1 ,# raph 1: Hi't3ra" A&i Re'pn'e !i"e'
Alice Chen (ac48272) PHY 117M (59065) 2/10/14
´ x
´ x
´ x
´ x
´ x
0#5
125
0
112
0#4
100
5 87# Pr$a$ilit en'it (1/10000) 0#4
5
Pr$a$ilit
0
75#
0#,
0
5
62#
0#,
5
0
50#
0#2
0
Audio Response Times
4# Percenta3e "ea'&re"ent' $eteen Percenta3e "ea'&re"ent' $eteen
´ ' an x´ ': 80; x ´ 2' an x´ 2': 90; x
Alice Chen (ac48272) PHY 117M (59065) 2/10/14 n rer t eter"ine the "ean an 'tanar e*iatin' a hi't3ra" that ha*e ne*er 'een $ere< &l l= i the "e the i'tri$&tin a' appr>i"atel nr"al< then eter"ine the 'tanar e*iatin $ ?nin3 the ran3e the i'tri$&tin that cntaine a$&t 80; the "ea'&re"ent' an i*iin3 it $ t# 5# Ran" 'a"ple 20 a&i re'pn'e ti"e "ea'&re"ent' 157 1,9 128 150 1,6 120 1,, 127 100 298 199 148 201 140 1,6 154 1,, 1,1 1,7 414 Mean (ms) 164#05 Mean -
∑ X n
Standard Deviation (ms) 72#1, -
157
+ 139+ 128+ 150 + 136+ 120 + … + 414 20
∑ ( x − x´ )
2
%tanar .e*iatin 2
-
n −1 2
2
2
( 157 −164 ) +( 139−164 ) +( 128−164 ) + … +( 414 −164 ) 19
PHY 117M< 'prin3 2014 58055 Ariel Chen (ac47,86) @a$ partner': .iana nti*er' Marian A&?er 6# !a$le 4: B*al&e' r $&narie' 2 an 1 'tanar e*iatin' aa r" the "ean x x x x ´ 2' ´ ' ´ ' ´ 2' D&nar +al&e 49#, 101#1 204#8 256#6 B*al&e 2 1 1 2 B-
x − x´ s
-
49.3−153 51.8
- 2
7# !alle't $ar in hi't3ra": 1,0170 Pr$a$ilit that a ran"l ch'en "ea'&re"ent a&i re'pn'e ti"e ill all $eteen 1,0 an 170 "': Z(130) =
130
−153
51.8
= -0.444
P(x<130, z<-0.444) = 0.2296 Z(170) =
170
−153
51.8
= -0.328
P(x<170, z<-0.091) = 0.4641 P(130
0.2345
8# .e'pite the act that '"e the ata i' 'i"ilar< it 'ee"' clear that the hi't3ra" ata pint' cllecte a' nt a nr"al i'tri$&tin# n a nr"al i'tri$&tin< the prprtin ata pint' that all ithin ne 'tanar e*iatin the "ean i' 68#5;< hich i' *er 11; ler than the e'ti"ate prprtin in the pltte hi't3ra"# !he act that the hi't3ra" i' nt nr"all i'tri$&te< e*en th&3h the 'hape the 3raph *er r&3hl re'e"$le' a nr"al i'tri$&tin< "a $e attri$&te t the act that the 'a"ple 'iEe i' nt lar3e en&3h t en'&re a nr"al 'hape# 9# Cn?ence inter*al' in relatin t "ean< ith ata ta=en r" a&i reactin ti"e' ith a "ean 152#95 "' an a 'tanar e*iatin 51#8 "'#
PHY 117M< 'prin3 2014 58055 Ariel Chen (ac47,86) @a$ partner': .iana nti*er' Marian A&?er
raph ,: 95; le*el cn?ence (>2F G >2F)
10# !he "ean (hriEntal line) 'h&l cr'' the percenta3e line' that inicate the le*el cn?ence e ha*e that the "ean i' the tr&e "ean# the *al&e'
PHY 117M< 'prin3 2014 58055 Ariel Chen (ac47,86) @a$ partner': .iana nti*er' Marian A&?er are 3raphe at 50; cn?ence< e 'h&l e>pect that the "ean (hriEntal line) 'h&l cr'' 50; the pint' ith errr $ar'# n the ?r't 3raph< the line cr''e' 16/20 the errr $ar'< r 80;# %ince e e>pecte the line t cr'' 68; the line'< the re'< i' hi3her than the e>pectatin# n the 'ecn 3raph< the line cr''e' 18/20 the errr $ar'< r 90;# %ince e e>pecte the line t cr'' 95; the line'< the re'< i' 'li3htl ler than the e>pectatin< $&t it i' 'till cl'e 11# Ater c"parin3 the "ean' r" the three e>peri"ent'< e cant $e 95; cn?ent that e ha*e $'er*e a real iIerence $eteen the ieal *al&e' " '&$Ject' reactin ti"e in the iIerent 'it&atin'# a.
$o"%ari! a&'io res%ose ti"e a' si"%e is&a res%ose ti"e
´ = x´ a− ´y v - 15, 242# - ,5# "' D ´s D =√ ´s a +´sv - √ 77.2 + 44.7 - 89#2 "' ´ −2 ( ´s D ) , D ´ 2( ´s D ¿ L 95; cn?ence - K D 2
2
2
2
Cn?ence inter*al - (21,#< 14,#) %ince 0 lie' in the inter*al< cannt $e 95; cn?ent there i' a real iIerence $eteen the ieal *al&e' " '&$Ject' reactin ti"e in the a&i an 'i"ple *i'&al re'pn'e ti"e'# b. $o"%ari! si"%e is&a res%ose ti"e (s) a' is&a *ith +hoi+e (+) res%ose ti"e ´ = x´ sv − y´ vc = 242. 327. = -8. "s D
´s D =√ ´s sv +´s vc
√ 44.7 +70.3 = 83.3 "s ´ −2 ( ´s D ) , D ´ 2( ´s D ¿ L 95; cn?ence - K D 2
2
=
2
2
$oi'e+e itera = (-22., 81.6)
%ince 0 lie' in the inter*al< cannt $e 95; cn?ent there i' a real iIerence $eteen the ieal *al&e' " '&$Ject' reactin ti"e in the 'i"ple *i'&al re'pn'e an *i'&al ith chice re'pn'e ti"e'#
