Question

There have been complaints that resident physicians and nurses at the rwj hospital desk respond slowly to emergency calls from senior citizens who are medical patients. it is claimed that it takes 10 minutes for non-senior patients to receive service. a researcher randomly selected 100 senior citizens and found that on average it took 12 minutes for the selected group of patients to receive proper medical response with the standard deviation of 6 minutes. at the 95% level of confidence can it be concluded that response time to emergency calls from senior citizens is longer than the other patients (use ci)?

Answer 1

A one-sample t-test is used to determine if the response time for senior citizens is longer than that for non-seniors. With a sample mean response time of 12 minutes and a standard deviation of 6 minutes for a sample of 100 senior citizens, the t-score calculation indicates a rejection of the null hypothesis at the 95% confidence interval.

Step-by-step explanation:

To determine if the response time to emergency calls from senior citizens is significantly longer than the response time to those from non-senior patients, we can use a one-sample t-test for the mean. We are comparing the sample mean response time for senior citizens (12 minutes) to a known population mean (10 minutes). The hypothesis tested is:

H0: μ = 10 (The mean response time for senior citizens is the same as non-seniors)
HA: μ > 10 (The mean response time for senior citizens is greater than non-seniors)

With a standard deviation of 6 minutes and a sample size of 100, the standard error (SE) is calculated as SE = 6 / √100 = 0.6. To calculate the t-score, we use the formula: t = (Sample Mean - Population Mean) / SE, giving us t = (12 - 10) / 0.6 = 3.33. We then compare the calculated t-score to the critical t-value from the t-distribution table at the 95% confidence interval (CI) for 99 degrees of freedom (since sample size - 1 = 100 - 1 = 99). If the calculated t-score exceeds the critical value, we reject the null hypothesis. In this case, the critical t-value is approximately 1.66. Since our t-score is greater than the critical value, we reject the null hypothesis and conclude that there is evidence at the 95% confidence level to support that the mean response time to emergency calls from senior citizens is longer than for non-senior patients.