Question

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**

1. The data fit the distribution for a fair six-sided die.

2. The data do not fit the distribution for a fair six-sided die.

Part (b)

State the alternative hypothesis. Choose 1 or 2

1. The data fit the distribution for a fair six-sided die.

2. The data do not fit the distribution for a fair six-sided die.

Part (c)

What are the degrees of freedom? (Enter an exact number as an integer, fraction, or decimal.)

Part (d)

What is the test statistic? (Round your answer to two decimal places.)

_______

What is the *p*-value? (Round your answer to four decimal
places.)

________

Part (e)

Alpha (Enter an exact number as an integer, fraction, or decimal.)

Answer #1

null hypothesis

1. The data fit the distribution for a fair six-sided die.

alternative hypothesis

The data do not fit the distribution for a fair six-sided die.

degrees of freedom = n-1 = 6-1 = 5

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 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...

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...

A six-sided fair die is rolled six times independently. If side
i is observed on the ith roll, it is called a match on the ith
trial, i = 1, 2, 3, 4, 5, 6. Find the probabilities that
(a) all six trials result in matches,
(b) at least one match occurs in these six trials,
(c) exactly two matches occur in these six trials.

A die is suspected of being biased. It is rolled 24 times with
the following results:
Outcome
1
2
3
4
5
6
Total
Outcome Probability
1/6
1/6
1/6
1/6
1/6
1/6
1
Expected Frequency
A
B
C
D
E
F
24
Observed Frequency
8
4
1
8
3
0
24
1) Conduct a significance test at a significant level of 5% to
see if the die is biased.
A die is not biased if the probability of each of...

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?

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

Example 1 A fair six-sided die is rolled six times. If the face
numbered k is the outcome on roll k for k=1, 2, ..., 6, we say that
a match has occurred. The experiment is called a success if at
least one match occurs during the six trials. Otherwise, the
experiment is called a failure. The sample space S={success,
failure} The event A happens when the match happens. A= {success}
Assign a value to P(A)
Simulate the experiment on...

A die is suspected of being biased. It is rolled 24 times with
the following results:
Outcome
1
2
3
4
5
6
Total
Outcome Probability
1/6
1/6
1/6
1/6
1/6
1/6
1
Expected Frequency
A
B
C
D
E
F
24
Observed Frequency
8
4
1
8
3
0
24
Conduct a significance test at a significant level of 5% to see if
the die is biased.
A die is not biased if the probability of each of the...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 3 minutes ago

asked 5 minutes ago

asked 5 minutes ago

asked 5 minutes ago

asked 7 minutes ago

asked 10 minutes ago

asked 12 minutes ago

asked 18 minutes ago

asked 41 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago