It is known that roughly 2/3 of all human beings have a dominant right foot or e

Question

It is known that roughly 2/3 of all human beings have a dominant right foot or eye. Is there also right-sided dominance in kissing behavior? An article reported that in a random sample of 133 kissing couples, both people in 83 of the couples tended to lean more to the right than to the left. (Use alpha = 0.05.) (a) If 2/3 of all kissing couples exhibit this right-leaning behavior, what is the probability that the number in a sample of 133 who do so differs from the expected value by at least as much as what was actually observed? () (b) Does the result of the experiment suggest that the 2/3 figure is implausible for kissing behavior? State the appropriate null and alternative hypotheses. H_0:P = 2/3 H_a: p notequalto 2/3 H_0: p = 2/3 H_a: p 2/3 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = State the conclusion in the problem context. Reject the null hypothesis. There is not sufficient evidence to conclude that the true proportion of right-leaning behavior differs from 2/3. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true proportion of right-leaning behavior differs from 2/3. Reject the null hypothesis. There is sufficient evidence to conclude that the true proportion of right-leaning behavior differs from 2/3. Do not reject the null hypothesis. There is sufficient evidence to conclude that the true proportion of right-leaning behavior differs from 2/3.

Explanation / Answer

here expected value =np=(133*2/3)=88.67

std deviation=(nP(1-p))1/2 =5.4365

hence P(X<=83) =P(Z<(83.5-88.67)/5.4365)=P(Z<-0.9504)=0.171

2) here p=2/3

hence std error =(p(1-p)/n)1/2 =0.0409

hence test stat z=(phat-p)/std error =(83/133-2/3)/0.0409 =-1.0423

p value =0.1486

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