Marvin Mccormick

2021-03-01

Explain the Chi – Square test.

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Skilled2021-03-02Added 95 answers

Step 1

Introduction:

The chi-square test can be used to test the in the following scenarios:

To test the Goodness of fit of the variables when their expected and observed frequencies are given.

To test the independence of the categorical variables by making it into a contingency table.

To test the significance of the single variance with the given variance.

1). Goodness of fit:

Goodness of fit test is applied to check how well the sample data obtained fits the distribution of the selected population. It can also be viewed as whether the frequency distribution fits the given pattern. Most commonly used test to check the goodness of fit is the chi-square test.

There are two values involved are observed and the expected values. The observed value represents the frequency of particular category in the sample and the expected value is obtained from the given distribution. Moreover, it summarizes the difference between the expected and observed values of the given data.

The hypotheses are stated as given below:

Null hypothesis: Data comes from the specified distribution.

Alternative hypothesis: Data does not come from the specified distribution.

The chi-square test statistic is calculated using the formula given below:

where,

Step 2

2). Test for independence:

In test for independence, we test whether there is an association between the categorical variables.

Null hypothesis: There is no association between the two categorical variables.

Alternative hypothesis: There is no association between the two categorical variables.

The chi-square test statistic is calculated using the formula given below:

where,

in

in

Step 3

3). Test for single variance:

Here, the chi-square test is used to compare the single sample variance with the population variance.

Null hypothesis: The given sample variance is equal to the population variance.

Alternative hypothesis: The given sample variance is not equal (less or greater) to the population variance.

The chi-square test statistic is calculated using the formula given below:

where,

n-Sample size

Step 4

Examples for some research questions based on chi square tests:

1.Is there significant association between blood pressure and exercise level?

2.Whether the class has less variation in statistics marks than the other past statistics classes marks?

3.To check whether health insurance benefits vary by the size of the company.

4.To test the claim that the subject distribution of books in the library fits the distribution of books checked out by students.

5.The level of education and the amount of proceeded foods in an individual’s diet are independent or not.

The product of the ages, in years, of three (3) teenagers os 4590. None of the have the sane age. What are the ages of the teenagers???

Use the row of numbers shown below to generate 12 random numbers between 01 and 99

78038 18022 84755 23146 12720 70910 49732 79606

Starting at the beginning of the row, what are the first 12 numbers between 01 and 99 in the sample?How many different 10 letter words (real or imaginary) can be formed from the following letters

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The ratio of radial probability density of finding an electron at $r={a}_{O}$ to the radial probability density of finding an electron at the nucleus is given as ($x.{e}^{-y}$). Calculate the value of (x+y).Find the sets $A$ and $B$ if $\frac{A}{B}=\left(1,5,7,8\right),\frac{B}{A}=\left(2,10\right)$ and $A\cap B=\left(3,6,9\right)$. Are they unique?

What are the characteristics of a good hypothesis?

If x is 60% of y, find $\frac{x}{y-x}$.

A)$\frac{1}{2}$

B)$\frac{3}{2}$

C)$\frac{7}{2}$

D)$\frac{5}{2}$The numbers of significant figures in $9.1\times {10}^{-31}kg$ are:

A)Two

B)Three

C)Ten

D)Thirty oneWhat is positive acceleration?

Is power scalar or vector?

What is the five-step process for hypothesis testing?

How to calculate Type 1 error and Type 2 error probabilities?

How long will it take to drive 450 km if you are driving at a speed of 50 km per hour?

1) 9 Hours

2) 3.5 Hours

3) 6 Hours

4) 12.5 HoursWhat is the square root of 106?