Question

The college bookstore tells prospective students that the average cost of its textbooks is $108 with a standard deviation of $4.50. A group of smart statistics students thinks that the average cost is higher. In order to test the bookstore’s claim against their alternative, the students will select a random sample of size 100. Assume that the mean from their random sample is $112.80.

1. Perform a hypothesis test (using R) at the 5% level of significance and state your decision. Also construct a 90% confidence interval (using R) for the average cost of textbook.
2. Perform the above task under the assumption that the students selected a random sample of size 10.
3. Write the difference between your findings of (1) and (2).

Answer 1

in both cases the null hypothesis is rejecting but the condidence interval in 2nd case is some wider than 1st bcs sample is small in 2nd case.