Question

Assume you toss a die 20 times and get the following values:

1,1,3,5,6,3,2,1,3,6,5,2,3,6,5,4,2,3,4,1

Use a Chi square test to check if it is a fair die or
no.

P-value is 0.05, use excel and consider the following
cases.

1- number of bins is 6

2-number of bins is 3

Answer #1

1)

p | Oi | Ei | (Oi-Ei)^2/Ei |

0.166666667 | 4 | 3.333333333 | 0.133333333 |

0.166666667 | 3 | 3.333333333 | 0.033333333 |

0.166666667 | 5 | 3.333333333 | 0.833333333 |

0.166666667 | 2 | 3.333333333 | 0.533333333 |

0.166666667 | 3 | 3.333333333 | 0.033333333 |

0.166666667 | 3 | 3.333333333 | 0.033333333 |

1 | 20 | 20 | |

TS | 1.6 | ||

5% | critical value | 11.07049769 | |

p-value | 0.901249345 |

p-value = 0.9012 > 0.05

hence we fail to reject the null hypothesis ,

we conclude that there is no sufficient evidence that die is not fair

2)

Oi | Ei | (Oi-Ei)^2/Ei |

7 | 6.666667 | 0.016666667 |

7 | 6.666667 | 0.016666667 |

6 | 6.666667 | 0.066666667 |

20 | TS | 0.1 |

critical | 5.991464547 | |

p-value | 0.951229425 |

You roll a die 48 times with the following results. Use a
significance level of 0.05 to test the claim that the die is
fair.
number: 1, 2, 3, 4, 5, 6
frequency: 2,4,12,13,14,3
test statistic
critical value
accept or reject

You wish to test the claim that a die is fair. You roll it 60
times with the following results. Number 1 2 3 4 5 6 Frequency 13
17 15 6 4 5 Find the value of the chi-square test statistic.

You get the data below by rolling a die 1,000 times. You want to
test if the distribution of outcomes is different than the
distribution of outcomes of a fair die. Use the Chi-squared
goodness of fit test and ?=.05.
1: 185
2: 150
3: 160
4: 140
5: 155
6: 210

You roll a die 48 times with the following results. Use a 0.05
significance level to test the claim that the die used is fair. Use
traditional method
NUMBER
FREQUENCY
1
13
2
3
3
12
4
15
5
2
6
3

A student rolled a supposedly fair die 60 times, resulting in
the distribution of dots shown. Research question: At
α = .10, can you reject the hypothesis that the die is
fair?
Number of Dots
1
2
3
4
5
6
Total
Frequency
9
16
11
12
6
6
60
Calculate the chi-square test statistic, degrees of freedom and
the p-value. (Round your test statistic value to 2
decimal places and the p-value to 4 decimal
places.)

A fair six-sided die is tossed twice. Consider the following
events:
1. A : First toss yields an even number.
2. B : Second toss yields an odd number.
3. C : Sum of two outcomes is even.
Find P(A), P(B), P(C), P(B ∩ C), P(C|B), P(C|A ∩ B) and
P(B|C).

A researcher wants to test whether a 6 sided die is not
fair. He rolled the die 2400 times and got the following
result:
one dot
two dots
three dots
four dots
five dots
six dots
530
430
730
439
150
121
Conduct a Chi Square Goodness-of-Fit analysis to test
that the die is not fair. Use the significance level of
0.05

You roll a fair die 5 times. What is the probability you get at
least four 6’s? This time you roll the die 204 times. What is the
probability you get between 30 and 40 6’s?

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 282 times and obtain the
following frequencies: (You may find it useful to reference the
appropriate table: chi-square table or F table)
Category 1 2 3
4 5 6
Frequency 64 57 46
38 38 39
Click here for the Excel Data File
a. Choose the...

A die is rolled 50 times and the following are the outputs:
6 1 3 4 2 6 3 5 1 3 6 1 6 6 3 3 6 5 2 4 1 6 5 3 1 2 5 2 1 2 4 1
4 1 5 5 6 6 2 1 1 2 5 6 5 5 6 3 1 3
What is the p-value of the chi-square test that the die is
unbiased?

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