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 127 kissing couples, both people in 82 of the couples tended to lean more to the right than to the left. (Use = 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 127 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.)
_____________

(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.

H0: p = 2/3
Ha: p 2/3H0: p = 2/3
Ha: p < 2/3    H0: p = 2/3
Ha: p 2/3H0: p = 2/3
Ha: p > 2/3 [Correct]

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.)

Explanation / Answer

(a) If 2/3 of all kissing couples exhibit this right-leaning behavior, what is the probability that the number in a sample of 127 who do so differs from the expected value by at least as much as what was actually observed?

Answer : sample proportion = 82/127 = 0.646

(b) H0 : p = 2/3

Ha : p    2/3

(c) standard error of proportion se0 = sqrt (2/3 * 1/3 * 1/127) = 0.04183

Z = (p^ - 2/3)/ se0 = (82/127 - 2/3)/ 0.04183 = -0.50

p- value = 2 * Pr(Z < -0.50) = 2 * 0.3085 = 0.6170

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