Question

Constanca hears the news that 25% of all college students in the US dont know the capital of the Portugal. SHe randomly picks 50 students and finds that 10 of them cannot name the capital of Portugal. Is this significantly different tha the reported percentage at the 1% level of significance?

Answer 1

Let p denotes the true proportiom of college students in the US dont know the capital of the Portugal.

To test against

Here

sample proportion

and sample size n = 50

The test statistic can be written as

which under H₀ follows a standard normal distribution.

We reject H₀ at 1% level of significance if

Now,

The value of the test statistic

and critical value

Since , so we fail to reject H₀ at 1% level of significance and we can conclude that the reported percentage is not significantly different from 25%.