1. An experiment is run that is claimed to have a binomial distribution with p = 0.15 and n = 18 and the number of successes is recorded. The experiment is conducted 200 times with the following results:
|
Number of Successes
|
0
|
1
|
2
|
3
|
4
|
5
|
|
Observed Frequency
|
80
|
75
|
39
|
6
|
0
|
0
|
Using a significance level of 0.01, is there sufficient evidence to conclude that the distribution is binomially distributed with p = 0.15 and n = 18?
2. Data collected from a hospital emergency room reflect the number of patients per day that visited the emergency room due to cardiac-related symptoms. It is believed that the distribution of the number of cardiac patients entering the emergency room per day over a two-month period has a Poisson distribution with a mean of 8 patients
per day.
|
6
|
7
|
9
|
7
|
5
|
6
|
7
|
7
|
5
|
10
|
|
9
|
9
|
7
|
2
|
8
|
5
|
7
|
10
|
6
|
7
|
|
12
|
12
|
10
|
8
|
8
|
14
|
7
|
9
|
10
|
7
|
|
4
|
9
|
6
|
4
|
11
|
9
|
10
|
7
|
5
|
10
|
|
8
|
8
|
10
|
7
|
9
|
2
|
10
|
12
|
10
|
9
|
|
8
|
11
|
7
|
9
|
11
|
7
|
16
|
7
|
9
|
10
|
Use a chi-square goodness-of-fit test to determine if the data come from a Poisson distribution with mean of 8. Test using a significance level of 0.01.