PSTAT 5A
Unit 7 & 8 Practice Problems
1. In a study of 1907 fatal traffic accidents, 449 were alcohol related. Construct a 99%
confidence interval for the population proportion of fatal traffic accidents that are alcohol
related.
2. You wish to estimate the proportion of students who will vote for Timmy for ASB student
body president at a 95% level of confidence. Find the minimum sample size needed to be
accurate to within 4% of the population proportion. Use a preliminary estimate of p =
0.515.
3. A communications spokesperson claims that over 48% of Americans either own a cellular
phone or have a family member who does. In a random survey of 984 Americans, 471
said they or a family member owned a cellular phone. Test the spokesperson claim at a
5% significance level. What can you conclude?
4. In a poll of 120 Congress members, it was found that 72 support a certain controversial
change in tax laws. We are interested in estimating the proportion of all Congress
members that support the controversial change in tax laws.
A. What distribution should we use for this analysis?
B. Define the PARAMETER and RANDOM VARIABLE of interest.
C. Construct a 95% confidence interval for the proportion of all Congress members
that support this change.
D. Interpret the confidence interval found in part C.
5. An experiment on the side effects of pain relievers assigned 440 randomly chosen arthritis
patients to receive a brand of pain reliever. 55 out of the 440 arthritis patients
experienced adverse side effects from this medication. The company that produces this
pain reliever claims that less than 10% of the patients who take this medication have
adverse symptoms. Test the claim using a 5% significance level.
6. In a random sample of 300 graduating male UCSB students, it was found that 28 were
planning to leave the state. In a random sample of 500 graduating female UCSB students,
it was found that 58 were planning to leave the state. A college administrator wants to
determine whether there is any significant difference between the two populations.
A. Identify the PARAMETER and RANDOM VARIABLE of interest for each population.
B. Determine the appropriate distribution for the analysis.
C. Find a 95% confidence interval for the difference between the two population
proportions. Is there a difference? Explain.
7. In a survey of 342 High School students attending private schools, 92 participate in a
varsity sport. In a survey of 513 High School students attending public schools, 150
participate in a varsity sport. Can you support the claim that the proportion of students
participating in varsity sports at private schools is no more than the proportion in public
schools? Use a 1% significance level.