Nationally, patients who go to the emergency room wait an average of 5 hours to be admitted into the hospital. Do patients at rural hospitals have a higher waiting time? The 15 randomly selected...

Nationally, patients who go to the emergency room wait an average of 5 hours to be admitted into the hospital. Do patients at rural hospitals have a higher waiting time? The 15 randomly selected patients who went to the emergency room at rural hospitals waited an average of 5.7 hours to be admitted into the hospital. The standard deviation for these 15 patients was 2.7 hours. What can be concluded at the the αα = 0.01 level of significance level of significance?

1. For this study, we should use the z-test for a population proportion or t-test for a population mean


2. The null and alternative hypotheses would be:

 H0:H0:  ? μ p  Select an answer = < ≠ >

 H1:H1:  ? μ p  Select an answer > <>

1. The test statistic ? z or t  =  (please show your answer to 3 decimal places.)


2. The p-value =  (Please show your answer to 4 decimal places.)


3. The p-value is ? ≤ >  αα


4. Based on this, we should accept, fail to reject or reject  the null hypothesis


5. Thus, the final conclusion is that ...
   
   
   

   
   
   • The data suggest the population mean is notsignificantly higher than 5 at αα = 0.01, so there is statistically insignificant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is equal to 5 hours.
   
   
   • The data suggest the populaton mean issignificantly higher than 5 at αα = 0.01, so there is statistically significant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is higher than 5 hours.
   
   
   • The data suggest that the population mean awaiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is notsignificantly higher than 5 hours at αα = 0.01, so there is statistically insignificant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is higher than 5 hours.