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Chapter 6, Section 3-HT, Exercise 162 Babies Learn Early Who They Can Trust A study 1 indicates that babies may choose not to learn from someone they dont trust. A group of 60 babies, aged 13 to l6 months, were randomly divided into two groups. Each baby watched an adult express great excitement while looking into a box. The babies were then shown the box and it either had a toy in it (the adult could be trusted) or it was empty (the adult was not reliable.) The same adult then turned on a push-on light with her forehead, and the number of babies who imitated the adults behavior by doing the same thing was counted. The results are in Table 1. Test at a 5% level to see if there is evidence that babies are more likely to imitate those they consider reliable. Imitated 18 10 Table 1 Baties invtate those they trust Did not imitate 12 20 Reliable Unreliable
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Step1: The first sample size is n 30 Step2: The number of subjects that are reliable is The number of subjects that are unreliable is The second sample size is 30 X 10 30 0.60 p,-0.60 1 0.60 0.40 1 0.40 Step3 10 30 -0.30 p,-0.30 1-0.30 0.70 920.70 (a) Step4: State the null and altemative hypotheses In other words, we are to test whether p, is greater than p2. This can be written as P P2 Thus, the two hypotheses are H0 : p,-p2 or pl-p2-0 (p1 1s equal to p2 P>P2 or -P2 >0 (pi is greater than P2 Step5: Select the distributi on to use AP1.4%-ぬPa and z292 are all greater than 5, Consequently both samples are large, and we use the normal distributi on to make the test Step6: Determine the rejecti on and non-rejection regions The > sign in the alternative hypothesis indicates that the test is right-tailed. From the normal distributi on table for a 0.05 significance level, the critical value of z is 1.645

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