Question
In: Statistics and Probability
Let X equal the number of female children in a three-child family. Among students who were...
Let X equal the number of female children in a three-child family. Among students who were taking statistics, 52 came from families with three children. For these families x = 0, 1, 2, and 3 for 5, 17, 24, and 6 families, respectively.
(a) Conduct a Chi-square goodness-of-fit test to test the null hypothesis that the distribution of X is B(3, 0.5) at 0.05 significance level.
(b) Conduct a Chi-square goodness-of-fit test to test the null hypothesis that the distribution of X is B(3, p) at 0.05 significance level. Estimate p.
Solutions
orchestra answered 1 year agoRelated Solutions
9.1-5. Let X equal the number of female children in a three-child family. We shall use...
9.1-5.
Let X equal the number of female children in a
three-child family. We shall use a chi-square goodness-of-
fit statistic to test the null hypothesis that the
distribution
of X is b (3, 0.5).
(a)
Define the test statistic and critical region, using an
α = 0.05 significance level. (b)
Among students who were taking statistics, 52 came
from families with three children. For these families,
x= 0, 1, 2, and 3 for 5, 17, 24, and 6 families,...
Three fair coins are flipped independently. Let X be the number of heads among the three...
Three fair coins are flipped independently. Let X be the number
of heads among the three coins.
(1) Write down all possible values that X can take.
(2) Construct the probability mass function of X.
(3) What is the probability that we observe two or more heads.
(i.e., P(X ≥ 2))
(4) Compute E[X] and Var(X).
60 randomly selected students were asked how many siblings were in their family. Let X =...
60 randomly selected students were asked how many siblings were
in their family. Let X = the number of pairs of siblings in the
student's family. The results are as follows:
Siblings
Frequency
1
13
2
22
3
15
4
6
5
3
6
0
7
1
Round your answers to two decimal places.
The mean is:
The median is:
The sample standard deviation is:
The first quartile is:
The third quartile is:
What percent of the respondents have had...
54 randomly selected students were asked how many siblings were in their family. Let X -...
54 randomly selected students were asked how many siblings were
in their family. Let X - the number of pairs of siblings in the
student's family.
# of Siblings
0
1
2
3
4
5
Frequency
5
9
10
13
10
7
Round all your answers to one decimal place.
The mean is:
The median is:
The sample standard deviation is:
The first quartile is:
The third quartile is:
What percent of the respondents have at least 1 siblings?
_____%...
Let X be the number of students who attend counseling at a certain time of day....
Let X be the number of students who attend counseling at a
certain time of day. Suppose that the probability mass function is
as follows p (0) = .15, p (1) = .20, p (2) = .30, p (3) = .25, and
p (4) = .10. Determine:
a) Is this a valid probability mass function? Why?
b) Obtain the cumulative probability function
c) What is the probability that at least two students come to
counseling
d) What is the probability...
52 randomly selected students were asked how many siblings were in their family. Let X represent...
52 randomly selected students were asked how many siblings were
in their family. Let X represent the number of pairs of siblings in
the student's family. The results are as follows:
# of Siblings
0
1
2
3
4
5
6
Frequency
10
11
7
4
5
10
5
Round all your answers to 4 decimal places where
possible.
The mean is:
The median is:
The sample standard deviation is:
The first quartile is:
The third quartile is:
What percent...
let x be the number of smokers in a family composed of a husband and a...
let x be the number of smokers in a family composed of a husband
and a wife. X is a random variable which takes values 0,1,2, with
respective probabilities po, p1, p2. The average number of smokers
per family is 0.63. 40% of families contain at least one smoker.
find the probabilities po, p1, p2.
Note: this question is related to binomial distribution
lesson
In MAPLE or MATLAB A family with three children is chosen at random and the number...
In MAPLE or MATLAB
A family with three children is chosen at random and the number
X of daughters is counted. Describe how to
simulate an observation on X based on U ~
unif[0,1]. Then, simulate 20 observations on
X.
59 randomly selected students were asked the number of pairs of shoes they have. Let X...
59 randomly selected students were asked the number of pairs of
shoes they have. Let X represent the number of pairs of shoes. The
results are as follows:
Round all your answers to 4 decimal places where
possible.
The mean is:
The median is:
The sample standard deviation is:
The first quartile is:
The third quartile is:
What percent of the respondents have at least 12 pairs of Shoes?
%
53% of all respondents have fewer than how many pairs...
64 randomly selected students were asked the number of pairs of shoes they have. Let X...
64 randomly selected students were asked the number of pairs of
shoes they have. Let X represent the number of pairs of shoes. The
results are as follows:
# of Pairs of
Shoes
4
5
6
7
8
9
10
11
12
13
14
15
Frequency
4
4
3
7
2
5
10
5
5
8
6
5
Round all your answers to 4 decimal places where
possible.
The mean is:
The median is:
The sample standard deviation is:
The...
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