A couple of confidence intervals

In a survey of households, 45 of 120 randomly selected physicians were retrievers.  (It was supposed to be “dogs were retrievers”.  I was trying to make up a problem involving doctors.  Oops.)  Find a 90% confidence interval for the true proportion of dogs that are retrievers.



A random sample of 36 wait times for the ER at Local McHospital had a sample average of 53 minutes with a standard deviation of 10.  Find a 95% confidence interval for wait times at LMH’s ER.





Hypothesis tests examples.


The percentage of dogs that are retrievers is known to be 27.9% in a town with mandatory dog licenses.  Jim thinks his town (Dark Sky) has a higher percentage of retrievers.  In a survey of households, 45 of 120 randomly selected dogs were retrievers. Is there sufficient evidence at the 0.05 level of significance that backs Jim’s claim?



The US national average number of times that students eat macaroni as a meal in a semester is reported to be 36.  A professor at MU thinks our students are different.  A random sample of 24 MU students yielded a sample mean of 42.1 macaroni meals per semester with a standard deviation of 5.3. At the 0.01 level of significance, can it be concluded that this differs from the national average?  You may assume that the distribution of the number of times that students eat macaroni as a meal is normal.