Chi-Square Distribution and Its Applications

The given distribution of the number of defective blades produced in a single shift in a factory over $100$ shifts is given below.

Test whether the number of defective blades follows a Poisson distribution with mean =$0.44$ Use $\alpha =0.05.$ Test the null hypothesis and alternative hypoyhesis.

The quality grade of electric components produced in two factories is given in the table given below.

Test whether there is any association between factories and quality of grades. Test the $5\%$ level of significanceand test the null hypothesis and alternative hypothesis.

The given weights (in kg) of $10$students from a school are $38,40,45,53,47,43,55,48,52,49$. Than the variance of the distribution of weights of all students from the above school is equal to$20\mathrm{kg}$. Test the $5\%$ level of significance.

In a sample of $200$ households in a colony, two brands of hair oils A and B are applied by $90$, females. Further, $60$ females and $70$ males are using brand A. To test whether there is any association between the gender and brand of hair oil used, by constructing a contingency table and test the null hypothesis and alternative hypoyhesis.

Write the test statistic for$2 \times 2$ contingency tables.

Write down the computational steps for testing the significance of goodness of fit.

Write the test procedure for testing the independence of attributes

Discuss the procedure to test the population variance.

Define contingency table?

Discuss the properties of χ2 distribution in detail.

Give the recurrence formula for binomial distribution

Define an attribute.

What are the minimum requirements of chi-square test?

Write the applications of chi-square distribution.

Define chi-square statistic

For contingency table of order$(m \times n)$ given by the statistic $\chi 2$,  with usual notations,

Find the degrees of freedom of test statistic if chi-square is performed for testing goodness of fit to a data with $k$ classes on estimating ‘s’ parameters.

Find the variance of chi-square distribution if $n$ is the degree of freedom.

Find the degrees of freedom of the sampling distribution of the test statistic for testing $H_0 : {\sigma }^2 = {{\sigma }_0}^{2 }$ is where ${\sigma }^2$ is the variance of normal population.

Which of the following is used for testing the hypothesis concerning variance of a normal population.