Final answer:
To test the claim that the mean waiting time for patients to be seen in the emergency room is equal to 20 minutes, we can use a two-tailed t-test. The null hypothesis (H0) is that the mean waiting time is 20 minutes, and the alternative hypothesis (Ha) is that it is not equal to 20 minutes.
Step-by-step explanation:
To test the claim that the mean waiting time for patients to be seen in the emergency room is equal to 20 minutes, we can use a two-tailed t-test. The null hypothesis (H0) is that the mean waiting time is 20 minutes, and the alternative hypothesis (Ha) is that it is not equal to 20 minutes.
Step 1: Set up the hypotheses:
- H0: µ = 20 (mean waiting time is equal to 20 minutes)
- Ha: µ ≠ 20 (mean waiting time is not equal to 20 minutes)
Step 2: Calculate the test statistic:
- t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))
- t = (18.5 - 20) / (4 / sqrt(40))
- t ≈ -0.9382
Step 3: Determine the critical region:
- With a significance level of 0.10 and a two-tailed test, we divide the significance level by 2 to get 0.05 for each tail.
- We look up the critical t-value for a two-tailed test with 39 degrees of freedom and a significance level of 0.05, which is approximately ±2.024.
Step 4: Make a decision about the null hypothesis:
- If the test statistic falls within the critical region, we reject the null hypothesis. If the test statistic falls outside the critical region, we fail to reject the null hypothesis.
- Since -0.9382 does not fall within the critical region of ±2.024, we fail to reject the null hypothesis.
Step 5: Draw a conclusion:
- Based on the sample data, there is not enough evidence to support the claim that the mean waiting time for patients to be seen in the emergency room is different from 20 minutes at the 0.10 significance level.