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 121 kissing couples, both people in 77 of the couples tended to lean more to the right than to the left. (Use α = 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 121 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
H_a: p > 2/3H₀: p = 2/3
H_a: p < 2/3    H₀: p = 2/3
H_a: p ≤ 2/3H₀: 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.

Do not reject the null hypothesis. There is sufficient evidence to conclude that the true proportion of right-leaning behavior differs from 2/3.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 not sufficient evidence to conclude that the true proportion of right-leaning behavior differs from 2/3.

Answer 1

n = 121, x = 77

p̄ = x/n = 0.6364

p = 2/3 = 0.6667

(a) P( |p̄ -p| > (0.6364 - 0.6667))

= P(z > (0.6364 - 0.6667)/√(0.6667 * 0.3333/121))

= P( z > -0.71)

= 1- P(z < -0.71)

Using excel function:

= 1 - NORM.S.DIST(-0.71, 1)

= 0.761

(b) Null and alternative hypotheses.

H₀: p = 2/3
H_a: p ≠ 2/3

Test statistic:

z = (p̄ -p)/√(p*(1-p)/n) = (0.6364 - 0.6667)/√(0.6667 * 0.3333/121) = -0.71

p-value = 2*(1-NORM.S.DIST(ABS(-0.7079), 1)) = 0.4790

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.