Question

A four-sided die is rolled 90 times; the results are in the table below. Conduct a hypothesis test to determine if there is evidence that the die is unfair/weighted.

Face Value |
Frequency |

1 |
24 |

2 |
28 |

3 |
22 |

4 |
16 |

Which pair of hypotheses is correct?

A) Ho: The distribution is U(4).

Ha: The distribution is not U(4).

B) Ho: The die is fair.

Ha: The die is not fair.

C) Ho: The probability of each face is ¼.

Ha: At least one face has a different

probability.

D) All of the above are correct.

Which type of test should be used for this data?

A) Z-test

B) T-test

C) *χ**2*
-test

Compute the test statistic, round to 3 decimals.

*Test Statistic= _________________________*

Compute the p-value, round to 4 decimals (2 if you convert to %):

*p-value= _________________________*

Using a 5% significance level, which is the correct conclusion?

A) The data is evidence the die is fair.

B) The data is not evidence the die is not fair.

C) The data is evidence the die is not fair.

Answer #1

1)D) All of the above are correct.

2)

C) *χ**2* -test

3)

applying chi square goodness of fit test: |

relative | observed | Expected | residual | Chi square | |

category | frequency(p) |
O_{i} |
E_{i}=total*p |
R^{2}_{i}=(O_{i}-E_{i})/√E_{i} |
R^{2}_{i}=(O_{i}-E_{i})^{2}/E_{i} |

1 | 1/4 | 24 | 22.50 | 0.32 | 0.100 |

2 | 1/4 | 28 | 22.50 | 1.16 | 1.344 |

3 | 1/4 | 22 | 22.50 | -0.11 | 0.011 |

4 | 1/4 | 16 | 22.50 | -1.37 | 1.878 |

total | 1.000 | 90 | 90 | 3.3333 | |

test statistic X^{2} = |
3.333 |

frm excel:

p value = | chidist(3.333,3) = |
0.3430 |

since p value>0.05

B) The data is not evidence the die is not fair.

A six-sided die is rolled 120 times. Fill in the expected
frequency column. Then, conduct a hypothesis test at the 5% level
to determine if the die is fair. The data below are the result of
the 120 rolls. (Enter exact numbers as integers, fractions, or
decimals.)
Face Value
Frequency
Expected Frequency
1
14
?
2
32
?
3
15
?
4
15
?
5
30
?
6
14
?
Part (a)
State the null hypothesis. Choose 1 or 2...

A six-sided die is rolled 120 times. Fill in the expected
frequency column. Then, conduct a hypothesis test at the 5% level
to determine if the die is fair. The data below are the result of
the 120 rolls. (Enter exact numbers as integers, fractions, or
decimals.)
Face Value
Frequency
Expected
Frequency
1
14
?
2
33
?
3
15
?
4
14
?
5
30
?
6
14
?
Part (a)
State the null hypothesis. Choose 1 or 2...

#2) A six-sided die is rolled 120 times. The
data in the following table shows the results for 120
rolls:
Number of dots facing up
Frequency
Expected frequency
1
15
2
29
3
16
4
15
5
30
6
15
Fill in the expected frequencies
Use the data given to test the claim that the die is
fair (i.e. that the probabilities for each value are the...

A
regular four-sided die and a regular eight-sided die are rolled to
form a sum. a) Determine the probability distribution for the sum
of the two dice. Show Steps b) Create a frequency histogram for the
probability distribution. c) Determine the expected sum of the two
dice.

A fair 10-sided die is rolled 122 times. Consider the event
A = {the face 6 comes up at most 2 times}.
(a)
Find the normal approximation for P(A)
without the continuity correction.
(b)
Find the normal approximation for P(A)
with the continuity correction.
(c)
Find the Poisson approximation for P(A).

Assume that a fair
six-sided die is rolled 9 times, and the roll is called a success
if the result is in {1,2}{1,2}.
What is the probability that there are exactly 4 successes or
exactly 4 failures in the 9 rolls?

5. If a four-sided die is rolled 9 times, what is the
probability of getting exactly four 2s?
A. ≈ .0009 B. ≈ .0389 C. ≈ .0751 D. ≈ .1168 E. other
value
6. If a four-sided die is rolled, find the standard
deviation of the number showing. (Hint: First find the
variance.)
A. ≈ 1.12 B. ≈ 1.25 C. ≈ 2.50 D. ≈ 7.5 E. other
value
7. If a die is rolled 36 times, approximate the
probability of...

A fair 4-sided die is rolled 7 times.
(a)
Find the probability that the side 1 comes up exactly 3
times.
(b)
Find the probability that there is at least one side that comes
up exactly 3 times.

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.)

Alice rolled a fair, six-sided die ten times and counted that
she got an even number six times.
Which of the following statements is FALSE?
The distribution of the count of getting an
odd number is binomial.
The distribution of the count of getting an
even number is binomial.
The distribution of the count of getting an
even number cannot be modeled as approximately normal if the die is
rolled more than 100 times.
The distribution...

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