Ctr oints) 2- A person who plays craps (the game is rolling two dices) in a casi

Question

Ctr oints) 2- A person who plays craps (the game is rolling two dices) in a casino is suspicious that the dices that are used in casino are tampered with and therefore not fair. He takes a dice from the casino and conduct a test. He knows that the percentage of time that any face would show up in rolling a fair dice is 1/6 and that the mean of the numbers sho this dice 100 times and records the values. The mean of the data collected is 3.73 and the standard deviation of the sample is 1 89 Assuming 0.03, can you claim that the dice is not fair? Show all your work. No credit will be given if you do not show the work. If you use Excel, indicate the functions that you used. wing up is 3.33. He rolls

Explanation / Answer

Solution:

Here, we have to use one sample t test for population mean.

Null hypothesis: H0: Dice is fair.

Alternative hypothesis: Ha: Dice is not fair.

H0: µ = 3.33 versus Ha: µ 3.33

We are given

Xbar = 3.73

S = 1.89

n = 100

df = n – 1 = 99

We assume = 0.05

Test statistic formula is given as below:

t = (Xbar - µ) / [S/sqrt(n)]

t = (3.73 – 3.33) / [1.89/sqrt(100)]

t = 2.1164

Critical value = -1.9842 and 1.9842

P-value = 0.0368

(Critical value and P-value calculated by using t-table)

P-value < = 0.05

So, we reject the null hypothesis that Dice is fair.

At 5% level of significance, there is sufficient evidence to conclude that dice is unfair.

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