Question

Suppose in a survey of n = 400 students, 255 responded that they prefer small
classes and 145 responded that they prefer large classes. Let p denote the fraction
of all students who preferred small classes at the time of the survey, and ^ p be the
fraction of survey respondents who preferred small classes. (Hint: X is distributed
as a Bernoulli random variable)

1.Use the survey result to estimate p, and calculate the standard error of your
estimator. (Hint: Notice that this is the same as estimating the sample mean)
2.What is the p-value for the test H0 : p = 0:5 vs. H1 : p 6= 0:5? Will you reject
the null at the 5% significance level?
3.Construct a 95% confidence interval for p.

Answer 1