Which Formula do I use? Confidence Intervals

Four hundred randomly selected working adults in a certain state, included those who worked at hoe, were asked the distance from their home to their workplace. The average distance was 8.84 miles, with standard deviation 2.70 miles. Construct a 99% confidence interval for the mean distance from home to work for all residents of this state.

In order to estimate the proportion of entering students who graduate within six years, the administration at a state university examined the records of 600 randomly selected students who entered the university six years ago and found that 312 had graduated. Construct a 98% confidence interval for the six-year graduation rate.  

A sample of 26 women’s size 6 dressed had mean waste measurement 25.25 inches with sample standard deviation 0.375 inch. Construct a 95% confidence interval for the mean waist measurement of all size 6 women’s dresses. Assume waist measurements are normally distributed.  

In a study of dummy foal syndrome, the average time between birth and onset of noticeable symptoms in a sample of six foals was 18.6 hours, with a standard deviation of 1.7 hours. Assuming that the time to onset of symptoms in all foals is normally distributed, construct a 90% confidence interval for the mean time between birth and onset of noticeable symptoms.

In study of 12,447 hip replacements, 8% developed surgical site infection. Construct a 95% confidence interval for the proportion of all patients undergoing hip surgery who develop surgical site infection.  

A corporation that owns apartment complexes wishes to estimate the average length of time residents remain in the same apartment before moving out. A sample of 150 rental contracts gave a mean length of occupancy of 3.7 years with standard deviation 1.2 years. Construct a 95% confidence interval for the mean length of occupancy of apartments owned by this corporation.  

In study of 12,447 hip replacements, 8% developed surgical site infection. Construct a 95% confidence interval for the proportion of all patients undergoing hip surgery who develop surgical site infection.  

In the situation above, what is the value of q-hat?

In study of 12,447 hip replacements, 8% developed surgical site infection. Construct a 95% confidence interval for the proportion of all patients undergoing hip surgery who develop surgical site infection.  

In the situation above, what symbol is appropriate for the fraction of all surgeries developing surgical site infection.  

A sample of 26 women’s size 6 dressed had mean waste measurement 25.25 inches with sample standard deviation 0.375 inch. Construct a 95% confidence interval for the mean waist measurement of all size 6 women’s dresses. Assume waist measurements are normally distributed.  

In the situation above what symbol is appropriate for the mean waist measurement of all size 6 women’s dressed.  

A study examined the interactions in a​ children's museum.​ (Interactions by visitors to the museum included​ show-and-tell, learning,​ teaching, refocusing, participatory​ play, advocating, and disciplining​ interactions.) Researchers observed a sample of 164 meaningful​ interactions, of which 78 were led by children and 86 were led by adult caregivers.