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 118 kissing couples, both people in 73 of the couples tended to lean more to the right than to the left. (Use a = 0.05.) A USE SALT (a) If 2/3 of all kissing couples exhibit this right-leaning behavior, what is the probability that the number in a sample of 118 who do so differs from the expected value by at least as much as what was actually observed? (Round your answer to four decimal places.) (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. O Ho: p = 2/3 Hoip > 2/3 • Họ: p = 2/3 Hgip= 2/3 O Ho: p= 2/3 Hoip < 2/3 Hoi p = 2/3 H:ps 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.) P-value - State the conclusion in the problem context. • 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. O Reject the null hypothesis. There is sufficient evidence to conclude that the true proportion of right-leaning behavior differs from 2/3. O Reject the null hypothesis. There is not sufficient evidence to conclude that the true proportion of right-leaning behavior differs from 2/3. O Do not reject the null hypothesis. There is sufficient evidence to conclude that the true proportion of right-leaning behavior differs from 2/3.

Given info: It is known that nearly 2/3 of the human beings has a dominant right foot or eye. A random sample of 118 kissing couples was selected. Among them 73 of the couples tended to lean more to the right than to the left. Let X be the number of couples who lean more to the right when they kiss. Hence, X∼Bin(118,2/3). The expectation of X is, E(X)=n×p=118×2/3=78.667 V(X)=nxpxq =118x2/3x1/3=26.222 SD(X)=sqrt(26.222)=5.121From the sample, it was observed that the number of couples who lean more to right when they kiss is 73.b) Let p be the true proportion of couples who tended to lean more to the right than to the left. Null hypothesis: H0:p=2/3 Alternative hypothesis: Ha:p≠23 Test statistic: Procedure for one sample Z proportion test using TI-83+ calculator: Select STAT>TESTS>1-Prop z test Select Input as Stats Enter p0 as 0.667 x as 73 n as 113 And then select prop≠p0, select calculate. Output screen: From the above output, the test statistic value is -1.1146. The P-value is 0.265. Decision: If P-value≤α, reject the null hypothesis H0 If P-value>α, fail to reject the null hypothesis H0 Conclusion at α=0.05: Here, the P-value is greater than the level of significance. That is, P-value(=0.265)>α(0.05). By rejection rule, fail to reject null hypothesis. Interpretation: There is no evidence to suggest that the 2/3 figure is implausible for kissing behavior. That is, there is no sufficient evidence that the proportion of couples who tended to lean more to the right than to the left differs from 0.667 at 1% level of significance. Do not reject null hypothesis. there is not sufficient evidence to conclude that the true proportion right leaning behavior differs from 2/3.