Question

20. In a survey of 385 students at Broward College, North Campus, results revealed that 154 students were born outside of the USA and 231 were born in the USA. Using these results, test the claim at the .03 significance level that the proportion of students who are born outside of the USA is less than 35 percent. Be sure to show all the steps in the hypothesis testing procedure including the null and alternative hypotheses, the calculation of the test statistic, and correct wording of the final conclusion.

Answer 1

As we are testing here whether the proportion of students who are born outside of the USA is less than 35 percent, therefore the null and the alternate hypothesis here are given as:

The sample proportion here is computed as:

The test statistic here is computed as:

As this is a left tailed test, the p-value here is computed as:

p = P( Z< 2.0569 ) = 0.9802

Therefore the p-value here is 0.9802 > 0.03 that is the level of significance, therefore the test is not significant and we dont have sufficient evidence here that the proportion of students who are born outside of the USA is less than 35 percent.