Question

395 friends are smiling in their profile pictures. Of another independent random sample of 125 American friends, she found that 105 friends flashed a wide grin in her profie pictures Popolatios who are niling | proportion 1. China s95 2. United States Test the smiling in the Facebook profile pictures 35 t or 1,00 Select one n,> 0 O None of the other four (i) Test n 36 c answered out of 200 Select one. 1 o " 2.00 07220

Answer 1

Given that,

We used $\pi_2$ for Americans and $\pi_1$ for chinese

i) The null and the alternative hypotheses are,

$H_0: \pi_2 - \pi_1 \leq 0$

$H_1: \pi_2 - \pi_1 > 0$

Using TI-84 calculator we get,

ii) Test statistic is, Z^* = 1.25

iii) p-value = 0.1056

iv) Here, p-value = 0.1056 > $\alpha= 0.05$

So, we fail to reject the null hypothesis.

conclusion: conclude H₀ that the proportion of Americans is NOT larger than the proportion of chinese people who are smiling in their profile pictures.