Question

A hospital administrator randomly selects 80 patients and measured the time (in minutes) between when they checked in to the ER and the time they were first seen by a doctor. The average time is 142.8 minutes and the standard deviation is 37 minutes. She is getting grief from her supervisor on the basis that the wait times in the ER has increased greatly from last years average of 125 minutes. However, she claims that the increase is probably just due to chance.

(a) Perform a hypothesis test with significance level α=0.09 to see if wait times had increased.
H₀:μ=0
Hₐ:μ> 0

Answer 1

The p-value is less than the significance level (p < 0.09), so we reject the null hypothesis. There is sufficient evidence to conclude that the average wait time in the ER has increased.

Step-by-step explanation:

The null hypothesis (H₀: μ = 125) assumes that there is no significant change in the average wait time from the previous year. The alternative hypothesis (Hₐ: μ > 125) suggests an increase in average wait time. With a p-value less than the significance level (α = 0.09), we reject the null hypothesis in favor of the alternative.

The p-value represents the probability of observing a sample mean as extreme as 142.8 minutes, assuming the null hypothesis is true. In this case, the low p-value suggests that the observed increase in average wait time is unlikely due to random chance alone. Therefore, we have evidence to support the claim that the wait times have increased.

The significance level (α = 0.09) is the probability of rejecting a true null hypothesis. Since the p-value is less than α, we reject the null hypothesis. This decision is based on the idea that the observed data is not likely to have occurred if the null hypothesis were true, supporting the administrator's claim that the increase in wait times is not merely due to chance.

In conclusion, the statistical analysis provides support for the administrator's assertion that the increase in average wait time is significant. This information can be crucial for hospital management to address potential issues and improve efficiency in the ER.