In: Statistics and Probability

You roll a die 48 times with the following results.

Number |
1 |
2 |
3 |
4 |
5 |
6 |

Frequency |
3 |
1 |
15 |
13 |
4 |
12 |

Use a significance level of 0.05 to test the claim that the die is
fair.

**(PLEASE SHOW ALL YOUR WORK)**

**SOLUTION:**

From given data,

Doing an observed/expected value table,

O |
E |
(O-E)^{2} /
E |

3 | 8 | (3-8)^{2} / 8 = 3.125 |

1 | 8 | (1-8)^{2} / 8 = 6.125 |

15 | 8 | (15-8)^{2} / 8 = 6.125 |

13 | 8 | (13-8)^{2} / 8 = 3.125 |

4 | 8 | (4-8)^{2} / 8 = 2 |

12 | 8 | (12-8)^{2} / 8 = 2 |

Using ,

=

= 3.125+6.125+6.125+3.125+2+2

= 22.5

**Degree of freedom**

** = 6**

df = ** -1** = 6-1 =
5

significance level = = 0.05

**Critical value**

= 11.07049769

Also, the p value is

p = 0.000421

Thus, comparing and
[or, p and significance level], we REJECT THE NULL HYPOTHESIS.

There is significant evidence at 0.05 level that the die is not fair.

A die is rolled 60 times with the following results for the
outcomes 1, 2, 3, 4, 5, and 6, respectively: 13, 7, 6, 11, 10, and
13.
Specify the null and alternative hypotheses.
Use Minitab to perform the analysis. What is the
conclusion?
Show how to obtain by hand the found in the Minitab
output.
Demonstrate how to find the bounds on the p-value using a
table

You roll a balanced die two times. Is the second roll independent of the first roll?

You roll a die, winning nothing if the number of spots is
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c) You play 30 times. What is the probability that you win at
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what is the number of possible outcomes as a sum of successes?
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3) what is the probability you will roll 3 or 4 successes, of the
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4) what is the probability you will roll 3 or 4
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Suppose that you roll a die and your score is the
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A die was rolled 300 times. The following frequencies were
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Frequency 62 45 63 32 47 51
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PROJECT C
Roll a 6-sided die 800 times. If you do not desire to roll a
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