Question

The medical rehabilitation education foundation reports that the average cost of rehabilitation for

stroke victims is RM24672. To see if the average rehabilitation is different at a particular hospital, a
researcher selects a random sample of 35 stroke victims at the hospital and finds the average cost of
their rehabilitation is RM26343. The standard deviation of the population is RM3251. At 1% significance
level, can it be concluded that the average cost of stroke rehabilitation at a particular hospital is different
from RM24672.

Answer 1

To determine if the average cost of stroke rehabilitation at a particular hospital is different from RM24672, we conduct a hypothesis test using the given data. The test involves setting up hypotheses, calculating the test statistic, determining the critical value, making a decision, and stating the conclusion. Based on the data and the hypothesis test, there is enough evidence to conclude that the average cost of stroke rehabilitation at the particular hospital is different from RM24672 at a 1% significance level.

Step-by-step explanation:

To determine if the average cost of stroke rehabilitation at a particular hospital is different from RM24672, we can conduct a hypothesis test using the given data.

1. Step 1: Set up hypotheses:

• Null Hypothesis (H0): The average cost of stroke rehabilitation at the particular hospital is RM24672.
• Alternative Hypothesis (H1): The average cost of stroke rehabilitation at the particular hospital is different from RM24672.

Step 2: Choose a significance level, α. In this case, α = 0.01. Step 3: Calculate the test statistic:

• t = (mean of sample - population mean) / (standard deviation / √sample size)
• t = (26343 - 24672) / (3251 / √35)
• t ≈ 3.008

Step 4: Determine the critical value(s) or the p-value:

• This is a two-tailed test, so we need to compare the calculated t-value to the critical values from the t-distribution with degrees of freedom (df) equal to the sample size minus 1.
• Since the significance level is 0.01, we split it equally in the tails, resulting in a critical value of ±2.718.

Step 5: Make a decision:

• If the absolute value of the calculated t-value is greater than the critical value, we reject the null hypothesis.
• Since |3.008| > 2.718, we reject the null hypothesis.

Step 6: State the conclusion:

• Based on the data and the hypothesis test, there is enough evidence to conclude that the average cost of stroke rehabilitation at the particular hospital is different from RM24672 at a 1% significance level.