Question

Research conducted a few years ago showed that 38% of college students had traveled outside the US. A random sample of 140 international relations majors found that 68 have traveled abroad. Is there sufficient evidence, at the 0.05 significance level, to suggest that travel for international relations majors differs from that for the general population of college students? Is this test one-tailed or two-tailed? Why? State the null (H0) and alternative hypothesis (H1)What is/are the critical value(s)? Calculate the test statistic and decide whether or not to reject the null hypothesis. Summarize the results.

Answer 1

Solution :

This is the two tailed test because relations majors differs from that for the general population .

The null and alternative hypothesis is

H₀ : p = 0.38

H_a : p 0.38

= x / n = 68 / 140 = 0.4857

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.4857 - 0.38 / [(0.38 * 0.62) / 140]

= 2.577

P-value = 0.01

= 0.05

Critical values are : -1.96 , +1.96

Reject the null hypothesis .

There is sufficient evidence to suggest that the travel for international relations majors

differs from that for the general population of college students .