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 124 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 124 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.) Enter a number (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: 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.) 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 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. Reject the null hypothesis. There is sufficient evidence to conclude that the true proportion of right-leaning behavior differs from 2/3

Answer 1

Given : n=124 , x=77

(a) p=x/n=77/124=0.621

(b) Hypothesis : $H_0:p=2/3$ Vs $H_a:p\neq 2/3$

The test statistic is ,

$Z=\frac{p-p_0}{\sqrt{\frac{p_0q_0}{n}}}\to N(0,1)$

$=\frac{0.621-\frac{2}{3}}{\sqrt{\frac{\frac{2}{3}(1-\frac{2}{3})}{124}}}=-1.08$

P value = $P(Z>|Z_{stat}|)=P(Z>1.08)=2*0.14007=0.2801$

Decision : Here , P-value = 0.2810 > $\alpha=0.05$

Therefore , do not reject Ho at 0.05 significance level.

Conclusion : 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.