Question

A recent study found out that college students average about 7 hours of sleep per night. However, researchers at an urban   college in a big city are interested in showing that their students sleep less than 7 hours on the average. The researchers       conducted a simple random sample of n=100 students on campus.        They found out that the students averaged 6.6 hours. The previous   studies showed that the population standard deviation (s) of the   nightly sleeps was 1.8 hours.

1. Write the null and alternative hypotheses in mathematical notation

2. Calculate a test statistics and p-value in R

3. Does this sample provide a convincing evidence that the average sleep time at this urban college is less than 7 hours at a significance level $\alpha$ of 0.05?

Answer 1