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 84 of the couples tended to lean more to the right than to the left. (Use a0.o5.) (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? (Round your answer to three decimal places.) X 0.408 (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 Ho: -2/3 Ho: p = 2/3 H,: 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.) 0.86 P-value-89-103907 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 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 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.

Explanation / Answer

p^ = 84/133

sd(p^) = sqrt(pq/n) = sqrt( 84/133 * (1-84/133) / 133) = 0.04182733

84/133 =0.631578

difference = 0.666666-0.631578 = 0.035088

P(|p^-p| > 0.035088)

= 1- P(-0.035088/0.04182733 < Z < 0.035088/0.04182733 )

= 1 - P(-0.83887 < Z< 0.83887)

= 1- P (0.83887<Z<0.83887 )=1 - 0.592 = 0.408

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