Question

3. A gambler was watching a dice game and noticed that one of the dice seemed to come up with a “3” more often than it should. He grabbed the die and rolled it 60 times. He got a “3” 15 times.

a) State the null hypothesis and make the null box. State the alternative hypothesis.

b) Find the z-statistic for testing whether the null hypothesis c) Find the corresponding P-value. What can you conclude?

Answer 1

a)

Let P be the true proportion of 3's.

The null and alternate hypothesis are:

b)

The test statistic value is given by:

c)

Since this is a righ tailed test, so the p-value is given by:

Let the level of significance be 5%.

Since p-value is less than 0.05, so we have sufficient evidence to reject the null hypothesis
H0.

Thus we can conclude that .