Question

Among 43,592 in-hospital patients who had cardiac arrest during the day, 23,549 survived. Among 27,963 patients at night, 7,804 survived. Use a 0.01 significance level to test the claim that survival rates are the same for day and night.

Answer 1

Answer:

Conclusion. The proportions are not equal. Therefore, survival rates are not the same for the day and night. Also, there's enough evidence to affirm that the rates of survival are higher during the date, compared to the night.

Step-by-step explanation:

First of all. Let's identify the problem: This is a hypothesis testing for a difference of proportions. Check out attached images to follow through the process.

Answer 2

Using the z-distribution, it is found that since the p-value of the test is less than 0.01, there is enough evidence to conclude that survival rates are different for day and night.

What are the hypothesis tested?

At the null hypothesis, it is tested if the proportions are the same, that is, the subtraction of them is 0, hence:

$H_0: p_D - p_N = 0$

At the alternative hypothesis, it is tested if the proportions are different, that is:

$H_1: p_D - p_N \neq 0$

What are the mean and the standard error for the distribution of differences?

For each sample, they are given as follows:

• $p_D = \frac{23549}{43592} = 0.5402, s_D = \sqrt{\frac{0.5402(0.4598)}{43592}} = 0.0024$

• $p_N = \frac{7804}{27963} = 0.2791, s_N = \sqrt{\frac{0.2791(0.6209)}{27963}} = 0.0025$

Hence, for the distribution of differences, they are given by:

• $\overline{p} = p_D - p_N = 0.5402 - 0.2791 = 0.2611$

• $s = \sqrt{s_D^2 + s_N^2} = \sqrt{0.0024^2 + 0.0025^2} = 0.0035$.

What is the test statistic?

The test statistic is given by:

$z = \frac{\overline{p} - p}{s}$

In which p = 0 is the value tested at the null hypothesis.

Hence:

z = 0.2611/0.0035

z = 74.6.

What is the p-value of the test?

Using a z-distribution calculator, with z = 74.6, with a two-tailed test, as we are testing if the proportion is different of a value, the p-value is of 0.

Since the p-value of the test is less than 0.01, there is enough evidence to conclude that survival rates are different for day and night.

More can be learned about the z-distribution at brainly.com/question/13873630

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