Question

Which possible statements about the chi-squared distribution are true?a) The statistic X^2, that is

Modeling data distributions
ANSWERED
asked 2021-01-19

Which possible statements about the chi-squared distribution are true?
a) The statistic \(X^{2}\), that is used to estimate the variance \(S^{2}\) of a random sample, has a Chi-squared distribution.
b) The sum of the squares of k independent standard normal random variables has a Chi-squared distribution with k degrees of freedom.
c) The Chi-squared distribution is used in hypothesis testing and estimation.
d) The Chi-squared distribution is a particular case of the Gamma distribution.
e)All of the above.

Answers (1)

2021-01-20
The chi-square distribution is one of the continuous probability distributions and has one parameter called degree of freedom. It is a positively skewed distribution and its domain is the set of non-negative real numbers.
The statement “The statistic, that is used to estimate the variance of a random sample, has a Chi-squared distribution” is correct as it is used in hypothesis testing for goodness of fit of the distributions to the data.
The statement “The sum of squares of independent standard normal random variables has a Chi-squared distribution with degrees of freedom” is correct as it is one of the properties of the chi-square distribution and the relationship between chi-square and standard normal distribution.
The statement “The Chi-squared distribution is used in hypothesis testing and estimation” is correct as it is used to test the goodness of fit of models, independence of attributes, equality of population variances, estimating confidence intervals for population variance and standard deviation.
The statement “The Chi-squared distribution is a particular case of the Gamma distribution” is correct as Gamma distribution with scale and shape parameters equal to 1 and 0.5 respectively reduces to Chi-square distribution with 2 degrees of freedom.
Therefore, all of the above statements are true about the Chi-squared distribution.
0
 
Best answer

expert advice

Need a better answer?

Relevant Questions

asked 2021-02-02

Determine which of the following functions \(\displaystyle{f{{\left({x}\right)}}}={c}{x},\ {g{{\left({x}\right)}}}={c}{x}^{{{2}}},\ {h}{\left({x}\right)}={c}\sqrt{{{\left|{x}\right|}}},\ \text{and}\ {r}{\left({x}\right)}=\ {\frac{{{c}}}{{{x}}}}\) can be used to model the data and determine the value of the constant c that will make the function fit the data in the table. \(\begin{array}{|c|c|} \hline x & -4 & -1 & 0 & 1 & 4 \\ \hline y & -32 & -2 & 0 & -2 & -32 \\ \hline \end {array}\)

asked 2020-11-30

Identifying Probability Distributions. In Exercises 7–14, determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied. Cell Phone Use In a survey, cell phone users were asked which ear they use to hear their cell phone, and the table is based on their responses (based on data from “Hemispheric Dominance and Cell Phone Use,” by Seidman et al., JAMA Otolaryngology—Head & Neck Surgery , Vol. 139, No.

5). \(\begin{array}{|c|c|}& P(x)\\ Left & 0.636 \\ Right & 0.304 \\ No\ preference & 0.060\end{array}\)

asked 2021-06-09

The following table represents the Frequency Distribution and Cumulative Distributions for this data set: 12, 13, 17, 18, 18, 24, 26, 27, 27, 30, 30, 35, 37, 41, 42, 43, 44, 46, 53, 58

\(\begin{array}{|c|c|} \hline \text{Class}&\text{Frequency}&\text{Relative Frequency}&\text{Cumulative Frequency}\\ \hline \text{10 but les than 20}&5\\ \hline \text{20 but les than 30}&4\\ \hline \text{30 but les than 40}&4\\ \hline \text{40 but les than 50}&5\\ \hline \text{50 but les than 60}&2\\ \hline \text{TOTAL}\\ \hline \end{array}\)

What is the Relative Frequency for the class: 20 but less than 30? State you answer as a value with exactly two digits after the decimal. for example 0.30 or 0.35

asked 2021-01-17

Use the table from the Theoretical Distribution section to calculate the following answers. Round your answers to four decimal places. \(P(x = 3)=?\)
\(P(1 < x < 4) = ?\)
\(P(x \geq 8) = ?\) Use the data from the Organize the Data section to calculate the following answers. Round your answers to four decimal places. \(RF(x = 3) = ?\)
\(RF(1 < x < 4) =?\)
\(RF(x \geq 8) = ?\) Discussion Questions 1. Knowing that data vary, describe three similarities between the graphs and distributions of the theoretical, empirical, and simulation distributions. Use complete sentences.

...