Question

You are hired by a gambler to test a standard die of six faces with the numbers 1 through 6 on the six faces. Specifically, the gambler wants you to test to see if the probability that the number “4” comes up is actually equal to 1/6. You toss the die 100 times and you get 20 “4”s. Perform the test at a significance level of 5%. (State the null and alternative hypotheses. Be sure to clearly state the “rejection region” for the test, and state your conclusion in words.)

Answer 1

Null hypothesis:

The proportion of 4 coming up is 1/6

Alternate hypothesis:

The proportion of 4 coming up is not equal to 1/6

alpha = 0.05

For two tailed test z_c = 1.96

Reject the null hypothesis id |Z| > 1.96

Sample proportion

Z = 0.894

Do not reject the null hypothesis since Z = 0.894 > z_c = 1.96

Hence the null hypothesis is not rejected

Hence, The proportion of 4 coming up is 1/6