Question

6. A researcher wishes to test the effect of early discharge of cardiac patients on their ability to cope at home. The researcher administers the coping scale to 10 cardiac patients who were discharged early and 10 patients who stayed in the hospital for a longer period of time. Higher scores indicate better coping. Based on the data given in the table below, can you conclude that early discharge has an effect on cardiac patients’ on ability to cope at home? Perform an appropriate test at α = 0.05.

Conditions	Data
Early discharge	23, 17, 22, 18, 20, 26, 16, 13, 21, 14
Regular discharge (staying in the hospital for longer period of time)	30, 27, 25, 20, 24, 32, 17, 18, 28, 29

• Which hypothesis test should be used?

 one-sample Z-test  one-sample t-test  independent-samples t-test  paired-samples t-test

• Step 1. State the hypotheses (both in words and in symbols)

• H₀:

• H₁:

• Step 2: α = 0.05
• Step 3: Make a decision.
• Step 4: State a conclusion (You should include the test statistic, p-value, effect size, and a verbal interpretation of the result).

Answer 1

Here we use paired-samples t-test.

The test hypotheses are

The level of significance is . The sample sizes are . The degrees of freedom is .

Here, the sample means are . The sample standard deviations are .

The test statistic is

The P-value of the test is

Since , we reject the null hypothesis. The means are different.

We can  conclude with 95% confidence that early discharge has an effect on cardiac patient's on ability to cope at home.