One Proportion Z Test Worksheet



One Proportion Z Test Worksheet Do all 5 steps, on a separate sheet of paper, for each problem.

1. A drug manufacturer claims that fewer than 10% of patients who take its new drug for treating Alzheimer’s disease will experience nausea. In a random sample of 250 patients, 23 experienced nausea. Perform a significance test at the 5% significance level to test this claim.

2. Drug use is becoming an increasingly large problem at the high school athletic level and more and more schools are beginning to employ randomized drug testing. If a student tests positive for illegal substances, he/she is removed from the athletic team, issued a one-week suspension and ordered to attend a substance abuse class. A local high school claim since administering drug tests, the percent of athletes using drugs in their school has dropped to 25%. In order to test this claim, a urine sample is administered to a random sample of 100 athletes at the school and 20 come back positive. Perform a significance test at the 1% significance level.

3. Any Boston Celtics fan or archrival knows that Shaquille O’Neal, one of the NBA’s most dominant centers of the last twenty years, always had difficulty shooting free throws. Over the course of his career, his overall made free-throw percentage is 53.3%. During this offseason, Shaq is working with an assistant coach on his free-throw technique. During the first 5 games of the next season, Shag made 26 of his 39 free-throw attempts. Do these results provide convincing evidence that Shaq has significantly improved his free-throw shooting? Carry out a significance test at the ά = 0.1 level.

4. A sample of 500 turtles applied to ninja turtle training program. 60 of the applications were female turtles. Test to see if the true proportion female turtles who applied to the ninja turtle training program is less than 15% with α=.05.

5. Drake Mallard believes that 83% of St. Conrad residents adore Dark Wing Duck “terror that flaps in the night.” To test this hypothesis Drake selected a sample of 100 residents of St. Conrad and found that 80% adored DW. At α=0.05, is there enough evidence to reject the claim?

6. Shooter believes that when the Huskers run the Picket Fence that Buddy “gets caught watching the paint dry” at least 25% of the time. Shooter then records the following data from two weeks of practices. Out of 47 times practicing the play, Buddy is “caught watching the paint dry” 11 times. Test Shooter’s claim at the 5% level of significance.

7. The standard treatment for a disease works in 0.675 of all patients. A new treatment is proposed. Is it better? (The scientists who created it claim it is. You – as an advocate for a patient or sales personnel for the company that eventually would market it – must be more skeptical. Where’s the data?) An initial clinical trial of n = 100 patients (of similar general health) is conducted: 77 people are cured. Assume the selection of patients is random. Test the claim that the new treatment works on more patients at the 1% significance level.

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