Question

it is based on chi square test. Test the statistics. Critical value is given. Find Ho and H1. Please help

Answer 1

To test whether the number of seedling survival is affected by the different concentrations of the fungicide (10 ppm and 30 ppm), we can use the chi-square test for independence. This test will help determine if there is a significant relationship between the variables.

The null hypothesis (H0) states that there is no association between the concentration of the fungicide and seedling survival. The alternative hypothesis (H1) states that there is an association between the concentration of the fungicide and seedling survival.

Here's how we can perform the chi-square test:

1. Set up the contingency table: Construct a 2x2 contingency table with the rows representing the concentrations (10 ppm and 30 ppm) and the columns representing the survival outcomes (e.g., survived and did not survive). Record the observed frequencies in each cell based on the experiment results.

   markdownCopy code         | Survived | Did not Survive |

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10 ppm | a | b |

30 ppm | c | d |

2. Calculate the expected frequencies: Under the assumption of independence, we need to calculate the expected frequencies for each cell. The expected frequency for each cell is given by the formula:

Expected frequency = (row total * column total) / total number of observations

Calculate the expected frequencies for each cell in the contingency table.

3. Calculate the chi-square statistic: The chi-square statistic is calculated using the formula:

chi-square = Σ [(O - E)^2 / E]

Where Σ represents the sum over all cells, O is the observed frequency, and E is the expected frequency.

Calculate the chi-square value based on the observed and expected frequencies.

4. Determine the degrees of freedom: The degrees of freedom (df) for a 2x2 contingency table is calculated as:

df = (number of rows - 1) * (number of columns - 1)

In this case, df = (2 - 1) * (2 - 1) = 1.

5. Determine the critical chi-square value: Using the significance level (α) and the degrees of freedom, consult a chi-square distribution table or use statistical software to find the critical chi-square value.

6. Compare the calculated chi-square value with the critical chi-square value: If the calculated chi-square value is greater than the critical chi-square value, we reject the null hypothesis (H0) and conclude that there is a significant association between the fungicide concentration and seedling survival. If the calculated chi-square value is less than or equal to the critical chi-square value, we fail to reject the null hypothesis and conclude that there is no significant association.

Performing the above steps will help you determine if the number of seedling survival is significantly affected by the different concentrations of the fungicid