8.56 Do students like statistics? All respondents out of a random sample of ten students in a college said that they like statistics. Now you want to estimate the proportion of students who like statistics in the whole college.

a. Find the sample proportion of students who like statistics.

b. Find the standard error of the estimate and interpret it.

c. Find a 95% confidence interval using the large-sample formula. Is it appropriate to use the ordinary largesample confidence interval to obtain an estimation for the population proportion?

d. Why is it not appropriate to use the ordinary largesample confidence interval in part c? Use a more appropriate approach and interpret the result.