PH 661 Biostatistics II – Winter 2021
Assignment 3 (Chapters 8 )
1. Researchers are interested in estimating the prevalence of the HPV vaccine among young
women aged 13-30. Recent national statistics have estimated the population prevalence
for the vaccine since its initiation in this demographic is 23%. The research team has
pooled together 67 women this age range, and determined that 24 have received the
vaccine.
A) Can we carry on our investigation assuming a normal approximation is possible in this
instance? Why or why not?
B) Create a standardized z-score for the estimate calculated by the research team.
C) What is the probability associated with finding the proportion in this study?
2. Researchers are interested in the popularity of the new HPV vaccine among a population
of university aged women. National data released last year indicates that the vaccine is
increasing in popularity, and 24% of young women and girls aged 11-25 have now been
estimated to have received at least one of the three shots associated with the vaccine.
Suppose researchers randomly sample 7 girls in the population, and 3 report having at
least one of the injections.
A) Can we carry out our calculation for the probability of seeing such an occurrence with an
approximation of normality?
B) Calculate the probability of observing such a result.
C) If we were to repeat the sample, how many women in this age range would we expect to be
vaccinated?
3. Researchers are interested in estimating the prevalence of maternal smoking habits while
pregnant. There are countless advertisements warning such behavior, and recent statistics
claim the prevalence of such behavior is quite low, at only 5%. Suppose the research
team is planning a study to promote further intervention to decrease what they believe is
a rising prevalence of the behavior. Suppose they sample 107 pregnant mothers in their
third trimester and determine that 12 mothers have smoked at least once during their
pregnancy.
A) Can the researchers carry out their analysis assuming an approximation to the normal
distribution is acceptable?
B) Calculate the probability of observing the results that were witnessed in the sample.
C) Determine the mean and standard deviation for the distribution under the assumptions made
in part A.
4. Recent research has suggested that adolescent drinking behaviors have escalated.
Assume national statistics presume that only 14% of adolescents aged 13-17 engage in
alcohol consumption. A sample of 58 participants in this age range is collected and 13
participants report consuming alcohol on a regular basis.
A) Can researchers carry out their analysis assuming an approximation to the normal
distribution is acceptable?
B) Calculate the probability of observing the results witnessed in the sample.
C) Determine the mean and standard deviation for the distribution under the assumptions made
in part A.
5. Researchers are concerned about the binge drinking behaviors at a local university among
members of Greek life organizations. Assume the college reported that binge drinking
was observed in 31% of students attending the university. The research team conducts a
sample of 213 students involved in a Greek life organization on campus, and finds that 94
have reported binge drinking behaviors at least once that year.
A) Can researchers carry out their analysis assuming an approximation to the normal
distribution is acceptable?
B) Calculate the probability of observing the results witnessed in the sample.
C) Determine the mean and standard deviation for this distribution under the assumptions made
in part A.
6. The prevalence of asthma in a population of adolescents residing in a community outside
of a chemical plant is 24%. Suppose researchers are interested in assessing the severity
of asthma in a sample, and collect information on 15 participants and find that 6
adolescents have a history of asthma.
A) Can researchers continue their investigation assuming an approximation to the normal
distribution is possible?
B) Calculate the probability of observing the results seen in the sample conducted by the
researchers.
C) Determine the mean and standard deviation for the distribution under the assumptions made
in part A.
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