Question

(Q24-Q27) An insurance company has gathered the information regarding the number of accidents reported per day over a period of 100 days. The data can be found on the fourth sheet labeled “Accidents” in the “INFO1020 Final Exam DataFile.xlsx”. With the data, you are conducting a goodness-of-fit test to see whether the number of accidents per day can have a Poisson distribution. 24.What is the expected frequency of exactly 2 accidents per day? 25.What is the Chi-square test statistics? Round the value to 4 decimal places, e.g., round 0.25645 up to 0.2565, and round 0.25643 down to 0.2564. 26.What is the p-value? 27.At the 10% level of significance, what is the conclusion of this test? Data: Accidents per day 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5

Answer #1

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

0.074273578 | 0 | 5 | 7.427358 | 0.79329233 |

0.193111303 | 1 | 18 | 19.31113 | 0.089019272 |

0.251044694 | 2 | 25 | 25.10447 | 0.000434738 |

0.217572068 | 3 | 24 | 21.75721 | 0.231193332 |

0.141421844 | 4 | 20 | 14.14218 | 2.426358046 |

0.122576511 | 5 | 8 | 12.25765 | 1.47887983 |

0.877423489 | 100 | 100 | 5.019177547 | |

260 | ||||

lambda | 2.6 | p-value | 0.413544221 |

lambda = 2.6

24).What is the expected frequency of exactly 2 accidents per day = 25.10447

25)TS = 5.0192

26)p-value = 0.4135

27)

we fail to reject the null hypothesis as p-value > 0.10

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(Q24-Q27) An insurance company has gathered the information
regarding the number of accidents reported per day over a period of
100 days. The data can be found on the fourth sheet labeled
“Accidents” in the “INFO1020 Final Exam DataFile.xlsx”. With the
data, you are conducting a goodness-of-fit test to see whether the
number of accidents per day can have a Poisson distribution.
24.What is the expected frequency of exactly 2 accidents per day?
25.What is the Chi-square test statistics? Round...

A civil engineer has been studying the frequency of vehicle
accidents on a certain stretch of interstate highway. Longterm
history indicates that there has been an average of 1.74 accidents
per day on this section of the interstate. Let r be a
random variable that represents number of accidents per day. Let
O represent the number of observed accidents per day based
on local highway patrol reports. A random sample of 90 days gave
the following information.
r
0
1...

Data on the number of occurrences per time period and observed
frequencies follow. Use α = .05 to perform the goodness of fit test
to see whether the data fit a Poisson distribution. Calculate the
the value of test statistic. Use the "Number of Occurences" as the
categories.
Number of occurrences
numbers
of frequency
0
39
1
30
2
30
3
18
4
3
a) 8.334
b) 1.30
c) 3.142
d)...

The probability distribution of the number of accidents in North
York, Ontario, each day is given by
x
0
1
2
3
4
5
P(x)
0.20
0.15
0.25
0.15
0.20
0.05
a) Based on this distribution, what would be the expected number
of accidents on a given day?
A: 1.81
B: 1.47
C: 2.15
D: 4.62
b) Based on this distribution, what is the approximate value of
the standard deviation of the number of accidents per day?
A: 2.15
B:...

The safety director of a large steel mill took samples at random
from company records of minor work-related accidents and classified
them according to the time the accident took place.
Number of
Number of
Time
Accidents
Time
Accidents
8 up to 9 a.m.
8
1 up to 2 p.m.
8
9 up to 10 a.m.
4
2 up to 3 p.m.
10
10 up to 11 a.m.
8
3 up to 4 p.m.
9
11 up to 12 p.m.
11...

QUESTION 1
The number of degrees of freedom for the appropriate chi-square
distribution in goodness of fit test is
A
n − 1
B
(r-1)(c-1)
C
a chi-square distribution is not used
D
k − 1
QUESTION 2
A goodness of fit test and test of independence is always
conducted as a
A
upper-tail test
B
left-tail test
C
middle test
D
lower-tail test
QUESTION 3
The number of degrees of freedom for the appropriate chi-square
distribution in a test...

The safety director of large steel mill took samples at random
from company records of minor work-related accidents and classified
them according to the time the accident took place.
Number of
Number of
Time
Accidents
Time
Accidents
8 up to 9 a.m.
5
1 up to 2 p.m.
6
9 up to 10 a.m.
10
2 up to 3 p.m.
9
10 up to 11 a.m.
8
3 up to 4 p.m.
9
11 up to 12 p.m.
18
4...

1)The test statistic for testing the significance for the
overall regression model follows the
normal distribution.
Student's t-distribution.
F-distribution.
chi-square distribution.
2)When testing for a normal distribution with the chi-square
goodness-of-fit test with a sample size of 240 observations, the
number of intervals needed to satisfy the minimum number of
expected frequencies is ________.
4
5
6
The sample size is too small to perform the chi-square
goodness-of-fit test.
3)
A chocolate chip cookie producer claims that its cookies average...

The following table contains the probability distribution for
the number of traffic accidents daily in a small town. Complete
parts (a) and (b) to the right.
Number of accidents daily (x)
P(X)
0 0.30
1 0.37
2 0.16
3 0.07
4 0.05
5 0.04
6 0.01
a. Compute the mean number of accidents per
day.
b. Compute the standard deviation.

For a Chi-Squared Goodness of Fit Test about a distribution that
has the following characteristics:
Category 1: 20%
Category 2: 30%
Category 3: 10%
Category 4: 15%
Category 5: 25%
complete the table and compute the test statistic.
Round to the fourth as needed.
Categories
Observed
Frequency
Expected
Frequency
1
123
2
205
3
75
4
116
5
164
Test Statistic =

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