1. After using an email spam detector on your computer for a while, you start wondering if it's actually working at all - It almost looks like it's randomly tagging things as spam or not-spam. So, you decide to test it. You send to yourself 50 emails that you know are spam, and 100 emails that you know are not-spam. Of the 50 truly spam emails, 40 are flagged as spam; of the 100 truly not-spam emails, 30 are flagged as spam.

a) What are the two categorical variables in this problem?

b) Write down the corresponding 2-way table.

c) What's the percentage of:

- not-spam emails that get flagged as not-spam?

- spam emails that get flagged as spam?

- not-spam-flagged emails that are truly not-spam?

- spam-flagged emails that are truly spam?

d) Starting with the question "Data data provide evidence that the spam detector works?", set-up H0 and Ha.

e) Assuming the null hypothesis is correct, find the expected counts.

f) Find the X^2 of the chi-squared test.

g) Assuming you have done things correctly, I can tell you that the area to the right of the X^2 (i.e., the p-value) is really small: 10^(-8). State your conclusion/answer to the original question, at significance level 0.01. Later, you can check the solution to see how you can get the p-value in R.