1) A doctor claims that less than 75% of the patients that he performs a knee replacement
surgery on return to work in the first 3 months after the operation. A sample of 50 patients
that had a knee replaced by the doctor showed that only 34 of them returned to work within 3
months of the surgery. Test the doctor’s claim at the 0.05 level of significance.

2) A researcher wants to determine what proportion of all high school students plans to attend
community college upon graduating. He has no idea of what the sample proportion will be.
How large of a sample is required in order to be 90% sure that the sample proportion is off by
no more than 2%?

3) Does a parent’s education level have anything to do with their involvement at their child’s
school? A random sample of 601 parents of elementary school children were asked about
their own education level and whether they volunteered at their child’s school. Here are the
results.
Education Level Volunteered at School Did Not Volunteer at School
Less than high school 27 122
High school graduate 56 124
Some postsecondary 45 67
College graduate 61 55
Graduate/professional 25 19
At the 0.01 level of significance, test the claim that educational attainment and volunteering at
school are independent.

4) The president of a college wants to determine the mean number of units that college
students take per semester. How large of a sample is required in order to be 99% sure that
a sample mean will be off by no more than 1.25 units? An initial study suggested that the
standard deviation is approximately 2.1 units.

5) Test the claim that the mean time required for high school students to run 1 mile is greater
than 7 minutes at the 0.05 level of significance. Here are the results of a random sample of
25 students.
7.3 7.7 9.2 8.8 7.6 7.2 6.6 6.4 8.0
7.5 7.5 7.7 8.1 8.6 6.8 6.9 7.5
7.3 7.8 8.2 10.4 11.6 7.2 7.7 7.0