Question

2. Research conducted a few years ago showed that 35% of UCLA students had travelled outside the US. UCLA has recently implemented a new study abroad program and results of a new survey show that out of the 100 randomly sampled students 42 have travelled abroad. Is there significant evidence to suggest that the proportion of students at UCLA who have travelled abroad has increased after implementing the study abroad program? Test at 5% significance level.

Answer 1

Answer:There is no significant evidence that the proportion of students increased

Solution:

$\hat{p}=\frac{42}{100}=0.42$

$p_0=0.35$

Test statistic: $Z=\frac{\hat{p}-p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}=\frac{0.42-0.35}{\sqrt{\frac{0.35×0.65}{100}}}=1.468$

Critical value (1-sided, α=0.05): $Z=1.645$

$Z_{test}<Z_{critical}$ , therefore there is no significant evidence that the proportion of students increased