I need to see if I am doing these problems correctly. I am more of a handwritten person so if you can show me how to write these out I would appreciate it for our teacher only shows us how to use a...

I need to see if I am doing these problems correctly. I am more of a handwritten person so if you can show me how to write these out I would appreciate it for our teacher only shows us how to use a calculator.

Nationally, patients who go to the emergency room wait an average of 7 hours to be admitted into the hospital. Do patients at rural hospitals have a lower waiting time? The 15 randomly selected patients who went to the emergency room at rural hospitals waited an average of 5.9 hours to be admitted into the hospital. The standard deviation for these 15 patients was 1.4 hours. What can be concluded at the the αα = 0.05 level of significance level of significance?

1. For this study, we should use


2. The null and alternative hypotheses would be:

 H0:H0:

 H1:H1:

1. The test statistic     =  (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      the null hypothesis.


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

   
   
   • 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 lower than 7 hours at αα = 0.05, 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 lower than 7 hours.
   
   
   • The data suggest the population mean is notsignificantly lower than 7 at αα = 0.05, 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 7 hours.
   
   
   • The data suggest the populaton mean issignificantly lower than 7 at αα = 0.05, 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 lower than 7 hours.