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The number of weather-related deaths that occurred in different months of a year is provided.

The null hypothesis is as follows:

Weather-related deaths occur equally frequently in different months.

The alternative hypothesis is as follows:

Weather-related deaths do not occur equally frequently in different months.

It is considered a right-tailed test.

If the test statistic value is greater than the critical value, then the null hypothesis is rejected, otherwise not.

Let the months of the year be denoted by 1, 2, 鈥�..,12 starting from January.

Observed Frequency:

The frequencies provided in the table are the observed frequencies. They are denoted by\(O\).

The following table shows the observed frequency for each month:

Expected Frequency:

It is given that the deaths should occur with the same frequency each month.

Thus, the expected frequency for each of the 12 months is equal to:

\(E = \frac{n}{k}\)

where

n is the total frequency

k is the number of months

Here, the value of n is equal to:

\(\begin{aligned}{c}n = 28 + 17 + ..... + 25\\ = 450\end{aligned}\)

The value of k is equal to 12.

Thus, the expected frequency is computed below:

\(\begin{aligned}{c}E = \frac{n}{k}\\ = \frac{{450}}{{12}}\\ = 37.5\end{aligned}\)

The table below shows the necessary calculations:

The test statistic is computed as shown below:

\[\begin{aligned}{c}{\chi ^2} = \sum {\frac{{{{\left( {O - E} \right)}^2}}}{E}\;\;\; \sim } {\chi ^2}_{\left( {k - 1} \right)}\\ = 2.407 + 11.207 + ....... + 4.167\\ = 269.1467\end{aligned}\]

Thus, \({\chi ^2} = 269.1467\).

The degrees of freedom are computed below:

\(\begin{aligned}{c}df = \left( {k - 1} \right)\\ = \left( {12 - 1} \right)\\ = 11\end{aligned}\)

The critical value of\({\chi ^2}\)for 11 degrees of freedom at 0.01 level of significance for a right-tailed test is equal to 24.725.

The corresponding p-value is approximately equal to 0.000.

Since the value of the test statistic is greater than the critical value and the p-value is less than 0.05, the null hypothesis is rejected.

There is enough evidence to conclude thatweather-related deaths do not occur equally frequently in different months.

The months of May, June, and July tend to have a disproportionately higher number of weather-related mortality, which is due to the increased number of vacations and outdoor activities during those months.