Exam
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
6) A sample of 200 smokers were asked at what age they started smoking. The mean age was 18.3 years. The population standard deviation is 4.35 years. Construct a 90% confidence interval for the mean age that all smokers begin smoking.
7) A random sample of 400 Spanish adults revealed that 143 were smokers. A random sample of 300 American adults revealed that 70 were smokers. At the 0.05 level of significance, test the claim that the proportion of Spanish adults that smoke is greater than the proportion of American adults that smoke.
8) To test the claim that the mean blood glucose level of women is 100 mg/dL, a researcher takes a random sample of 135 women. They had a mean blood glucose level of 108.3 mg/dL. (The population standard deviation is 3.4 mg/dL). Test the claim at the 0.05 level of significance.
9) A random sample of 50 bags of blue corn tortilla chips had a mean weight of 9.06 ounces,with a standard deviation of 0.05 ounces. A random sample of 50 jalapeno tortilla chips had a mean weight of 9.01 ounces, with a standard deviation of 0.03 ounces. At the 0.05 level of significance, test the claim that the mean fill of blue corn tortilla chip bags is the same as the mean fill of jalapeno tortilla chips.
10) A group of 9 concertgoers was selected at random. Before the concert they were given a hearing test, and then given another one after the concert. (The volume varied during the test, and the subject also had to state which ear the sound was in.) Here are the number of correctly identified sounds out of 10, both before and after the concert.
Person A B C D E F G H I
Before 9 10 9 8 8 9 9 9 8
After 8 8 9 6 6 7 10 8 5
At the 0.05 level of significance, test a person’s hearing is worse after being affected by the noise of a concert.
11) Construct a 90% confidence interval for the mean highway mileage for hybrid cars. A random sample of 8 hybrid cars had the following highway mileages in mpg.
36 41 37 45 50 40 32 39
12) Hole selections for professional golf courses are changed each day of a PGA tournament. Are any of the days set up to be more difficult or easier? Here are the scores of 7 golfers on the four days of a tournament.
Round 1 Round 2 Round 3 Round 4
63 65 68 65
66 67 68 67
66 67 70 67
70 65 66 69
67 68 69 67
68 67 70 67
68 67 67 70
At the 0.01 level of significance, test the claim that the mean scores produced by the
four different rounds are equal.
13) In a survey of 500 women, 120 said that Valentine’s Day was their favorite occasion to receive flowers. Construct an 88% confidence interval for the proportion of all women who feel that Valentine’s Day is their favorite occasion to receive flowers.
14) A 1970 study showed that of American married-couple families, 43% had no children, 18% had one child, 18% had two children and 21% had three or more children. A recent survey of 500 American married-couple families revealed that 267 had no children, 87 had one child, 96 had two children and 50 had three or more children. At the 0.01 level of significance, test the claim that the 1970 proportions are no longer valid.
15) A random sample of 400 Fresno State students revealed that 228 were female. Test the claim that more than 50% of Fresno State students are female using a 0.05 level of significance.
16) Here are the scores of 9 randomly selected students on a Math 21 exam.
62 68 73 75 78 80 83 88 94 Test the claim that the mean score on this exam for all students is above 70 at the 0.05 level of significance.
17) A random sample of 50 COS students contained 13 that owned an iPhone. A random sample of 200 Fresno State students contained 70 that owned an iPhone. Use these data to test the claim that the proportion of COS students who own an iPhone is the same as the proportion of Fresno State students who own an iPhone at the 0.05 level of significance.
18) Ten COS Math 21 students were asked how many hours they studied for their final. Here are their responses.
8 10 12 7 9 13 8 10 14 10
Twelve COS Math 200 students were asked the same questions. Here are their responses.
6 7 5 8 10 6
8 5 0 11 9 6
At the 0.05 level of significance, test the claim that the mean number of hours studied by Math 21 students is greater than the mean number of hours studied by Math 200 students.
19) Here are the scores of eight Math 21 students on their midterm exam and their final exam.
Student 1 2 3 4 5 6 7 8
Midterm 74 66 80 75 90 78 71 88
Final 83 72 95 85 95 89 80 96
Use the 0.05 level of significance to test the claim that Math 21 students improve their
scores from the midterm exam to the final exam.
