To test the null hypothesis that the colors of the balls occur with equal frequency, we can use the Chi-Square test. Here are the steps:

1. First, calculate the total number of balls. This is 8 (red) + 5 (green) + 15 (orange) + 12 (blue) = 40 balls.

2. If the colors occur with equal frequency, each color would have the same number of balls. So, we would expect each color to have 40/4 = 10 balls.

3. Now, calculate the Chi-Square statistic. This is done by summing the squares of the differences between the observed (actual) and expected frequencies, divided by the expected frequency, for each category (color).

Chi-Square = Σ [ (Observed-Expected)^2 / Expected ]

For red balls: (8-10)^2 / 10 = 0.4
For green balls: (5-10)^2 / 10 = 2.5
For orange balls: (15-10)^2 / 10 = 2.5
For blue balls: (12-10)^2 / 10 = 0.4

4. Add these all up to get the Chi-Square statistic: 0.4 + 2.5 + 2.5 + 0.4 = 5.8

So, the Chi-Square value is 5.8.

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To test the null hypothesis that the colors of the balls occur with equal frequency, we can use the Chi-Square test. Here are the steps:

1. First, calculate the total number of balls. This is 8 (red) + 5 (green) + 15 (orange) + 12 (blue) = 40 balls.

2. If the colors occur with equal frequency, each color would have the same number of balls. So, we would expect each color to have 40/4 = 10 balls.

3. Now, calculate the Chi-Square statistic. This is done by summing the squares of the differences between the observed (actual) and expected frequencies, divided by the expected frequency, for each category (color).

Chi-Square = Σ [ (Observed-Expected)^2 / Expected ]

For red balls: (8-10)^2 / 10 = 0.4
   For green balls: (5-10)^2 / 10 = 2.5
   For orange balls: (15-10)^2 / 10 = 2.5
   For blue balls: (12-10)^2 / 10 = 0.4

4. Add these all up to get the Chi-Square statistic: 0.4 + 2.5 + 2.5 + 0.4 = 5.8

So, the Chi-Square value is 5.8.

Knowee AI · Accepted Answer

To test the null hypothesis that the colors of the balls occur with equal frequency, we can use the Chi-Square test. Here are the steps:

1. First, calculate the total number of balls. This is 8 (red) + 5 (green) + 15 (orange) + 12 (blue) = 40 balls.

2. If the colors occur with equal frequency, each color would have the same number of balls. So, we would expect each color to have 40/4 = 10 balls.

3. Now, calculate the Chi-Square statistic. This is done by summing the squares of the differences between the observed (actual) and expected frequencies, divided by the expected frequency, for each category (color).

Chi-Square = Σ [ (Observed-Expected)^2 / Expected ]

For red balls: (8-10)^2 / 10 = 0.4
   For green balls: (5-10)^2 / 10 = 2.5
   For orange balls: (15-10)^2 / 10 = 2.5
   For blue balls: (12-10)^2 / 10 = 0.4

4. Add these all up to get the Chi-Square statistic: 0.4 + 2.5 + 2.5 + 0.4 = 5.8

So, the Chi-Square value is 5.8.

Q22. Suppose a person has 8 red , 5 green, 15 orange and 12 blue balls.Test the null hypothesis that the colors of the balls occure with equal frequency. What is Chi Square value you get?*5.65.685.865.8

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