Question

Agraduate student conacted an expertment n which 14tenmonthdd babes were asked to wath acirrter character mpt to ascend a haOntwo occanons se baby wh esses lhe duran tal b ma e nea。Onne mod anempt, the baby witnesses etmer a helper toy push the character up the hill or a hinderer toy prevent the character from making the ascent. The helper and hindener oys were show to each baby in a andom tashion for a eed amount eftirte. The baby was then placed in tont of each toy and alowed to choose which toy he or she wahed ๒piay nflin12 of he 14cases, te baby dose Pe hepe by pwh㈤hough-- (a) Why is it impotant so ranaomy expose the baby to the helger or hinderer toy OA. The randonness in the order of exposure is important to avoid bias ○ B. The tanoomness inte oer at exposre is mportant to make sure hat te babes see te heperfrst ad te oter har ○ c. The ranoress in order at exposure is important to salisty the codt ons of usrg te bidri"probab ty doibton OD. The randomness inthe orderofeposure is importat to mriman the end d he นเnie standard deviat nehromer trst (b) What would be the appropriate null and atermative hoypotheses ithe esearher is athempting to show that babies prefer helpers over hindere 0.5 H, (c) Use the binomial probebility fomula to determine the Plue for this sest alu(Round to three decimal places as needed What is the correct condlusion regarding the null hypotei Click to select your answers)

Answer 1

(a) Option A

The randomness in the order of exposure is important to avoid bias.

If there is a specific order, then the baby might be biased to select any one particular type of toy.

(b) p = 0.5

p > 0.5

Since the claim is that the babies prefer helper toys over the hinderers, the alternative hypothesis is that the proportion of helper toys picked will be greater than half.

(c) The probability of picking any type of toy, p' = 0.5

The baby picks helper toys 12 times i.e. x = 12

Since it is a right-tail test, the p-value will be the probability of the baby picking helper toys 12 times or more i.e.

P(X> = 12) = P(X=12) + P(X = 13) + P(X = 14)

Formula for binomial distribution is P(X = x) = $nCx*p'^x*(1-p')^(n-x)$

So, P(X >= 12) =P(X = 12) + P(X = 13) + P(X = 14) =

14C12 0.512 (10.5)(14-12) 14C13 *0.513 * (1 - 0.5)(14-14C14 0.511 * (1 -0.5)(14-14)

=

14 91 0.51414 * 0.514 + 1 0.5

=

106 x 0.514

= 0.00647

Since this value if much less than the generally chosen significance levels of 0.01 or 0.05, the null hypothesis can be rejected. There is sufficient evidence to conclude that the babies prefer the helper toys over the hinderers.