Question

Can you please answer the following question

You suspect that an unscrupulous employee at a casino has tampered with a die; that is, he is using a loaded die. In order to test this claim, you roll the die 200 times and obtain the following frequencies: (You may find it useful to reference the appropriate table: chi-square table or F table)

Click here for the Excel Data File

Category	1	2	3	4	5	6
Frequency	40	35	33	30	33	29

a. Choose the appropriate alternative hypothesis to test if the population proportions differ.

• All population proportions differ from 1/6.

• Not all population proportions are equal to 1/6.

b. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

c. Find the p-value.

• p-value < 0.01

• 0.01 ≤ p-value < 0.025

• 0.025 ≤ p-value < 0.05

• 0.05 ≤ p-value < 0.10

• p-value ≥ 0.10

d. At the 10% significance level, can you conclude that the die is loaded?

• Yes, since the p-value is less than significance level.

• Yes, since the p-value is more than significance level.

• No, since the p-value is less than significance level.

• No, since the p-value is more than significance level.

Answer 1

The statistical software output for this problem is:

Hence,

a) Not all population proportions are equal to 1/6.

b) Test statistic = 2.320

c) p-value ≥ 0.10

d) No, since the p-value is more than significance level.