PLUS Q Lock, Statistics: Unlocking the Power of Data, 2e tela I System Announcem

Question

PLUS Q Lock, Statistics: Unlocking the Power of Data, 2e tela I System Announcements PRINTER VERSION BACK NEX Chapter 6, Section 1-HT, Exercise 060 Do Babies Understand Probability? Can babies reason probabilistically? A study1 investigates this by showing ten- to twelve-month-old infants two jars of lollipop shaped objects colored pink or black. Each infant first crawled or walked to whichever color they wanted, determining their -preferred color. They were then given the choice between two jars that had the same number of preferred objects, but that differed in their probability of getting the preferred color; each jar had 12 in the preferred color and either 4 or 36 in the other color. Babies choosing randomly or based on the absolute number of their preferred color would choose equally between the two jars, while babies understanding probability would more often choose the jar with the higher proportion of their preferred color. Of the 24 infants studied, 18 chose the jar with the higher proportion of their preferred color. Are infants more likely to choose the jar with the higher proportion of their preferred color? Denison, S. and X, F. (2014). The origins of probabilstic inference in human infants, Cognition, 130: 335- 347. Denison, S (o) State the null and alternative hypotheses Ho:

Explanation / Answer

Given that,
possibile chances (x)=18
sample size(n)=24
success rate ( p )= x/n = 0.75
success probability,( po )=0.5
failure probability,( qo) = 0.5
null, Ho:p<0.5  
alternate, H1: p>0.5
level of significance, = 0.05
from standard normal table,right tailed z /2 =1.64
since our test is right-tailed
reject Ho, if zo > 1.64
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.75-0.5/(sqrt(0.25)/24)
zo =2.4495
| zo | =2.4495
critical value
the value of |z | at los 0.05% is 1.64
we got |zo| =2.449 & | z | =1.64
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: right tail - Ha : ( p > 2.44949 ) = 0.00715
hence value of p0.05 > 0.00715,here we reject Ho
ANSWERS
---------------
a.
null, Ho:p=0.5
alternate, H1: p>0.5
b.
p^ = x/n = 0.75
c.
test statistic: 2.4495 ~ 2.45
d.
p-value: 0.00715
f.
yes

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