Question

A random sample of 150 WCC students found that 68 of them were Latino/a.

a) At the 5% level of significance can we prove that over 40% of all WCC students are Latino/a? State and test appropriate hypotheses. State conclusions.

b) Find the p-value of the test in (a).

c) If an error was made in (a), what type was it?

Answer 1

The number of WCC students (n) is 150.

The number of WCC students that were Latino/a (x) is 68.

The sample proportion is given by,

(a):The researcher wants to prove that over 40% of all WCC students are Latino/a.

Let p be the population proportion.

The null and the alternative hypothesis can be stated as:

It is a left tailed test

The test statistic can be calculated as:

  

Therefore, the test statistic is 1.3325.

Using the standard normal table, the right tailed critical value obtained at 0.05 level of significance is 1.645.

Since, the test statistic (1.3325) is less than the critical value (1.645), so the decision is fail to reject the null hypothesis. Therefore, there is insufficient evidence to support that over 40% of all WCC students are Latino/a.

(b): Using the standard normal table, the p-value is given by,

Therefore, the p-value is 0.0918.

(c): In the study, if the false Ho accepted, then it is termed as type II error.

In the part (a), the result is statistically insignificant which means that the null hypothesis does not gets rejected. Therefore, it can be said that the researcher fails to bring the sufficient evidence in favor of the alternative hypothesis. Hence, the type II error was made in part a).