I. Simulate a binomial random variable. Consider a class with 60 students, and the probability that a student does not turn in a homework is 0.10 (a “success”). Assume all students are independent of all other students, and the probability does not change.(a) Use sample to simulate drawing 60 students who either do, or do not, turn in their homework, and then find the total (out of 60) who did not turn in their homework. You should return one number,X= total # of students out of 60 who did not turn in their homework.

A dorm at a college houses 1900 students. One​ day, 20 of the students become ill with the ​flu, which spreads quickly. Assume that the total number of students who have been infected after t days is given by:

N(t)=1900/1+25e^-0.65t

​a) After how many days is the flu spreading the​ fastest?

​b) Approximately how many students per day are catching the flu on the day found in part​ (a)?

​c) How many students have been infected on the day found in part​ (a)?

Borishphobia is an autosomal recessive inherited condition in humans that causes AP Biology students to go into convulsions whenever they see the Hardy-Weinberg formula. Complete dominance is the mode of inheritance for the alleles in this condition.

In a group of 300 AP Biology students, 97 had convulsions (because they had the condition) during their first Hardy-Weinberg Problem Set. (Assume that students are a representative sample of a population at Hardy-Weinberg equilibrium.)

What is the frequency of the borishphobia (b) allele in this population of students? How many students in this class are homozygous (BB) for this condition?

A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 225 students and finds that 45 of them are receiving financial aid. Using a 95% confidence interval, what is the upper limit of the confidence interval to estimate the true proportion of students who receive financial aid.  

Using a 95% confidence interval, what is the upper limit of the confidence interval to estimate the true proportion of students who receive financial aid.

A small public school in northern California experienced an outbreak of pertussis (whooping cough). Pertussis was observed to develop in 31 of 96 unvaccinated children, 26 of 489 vaccinated children, and 14 of 67 children with unknown vaccination status. Are the unvaccinated students and those of unknown vaccination status at higher risk of pertussis? Calculate the appropriate measure of excess risk for the unvaccinated students versus the vaccinated students and for those with unknown vaccination status versus the vaccinated students (i.e., the vaccinated students are the unexposed). Interpret your results in plain language.

A research is interested in whether the mean score on a particular aptitude test for students who attend rural elementary schools is higher than the score of elementary school students in general (ux=50), ox=10). She tests a random sample of 28 rural elementary school students and finds the sample mean to be 56.

Using alpha=.05, conduct the 8 steps hypothesis testing to determine whether the rural elementary school students have a significantly higher aptitude score than elementary students in general.

PROBLEM 3

The average grade point average (GPA) of undergraduate students in New York is normally distributed with a population mean of 2.8 and a population standard deviation of 0.75

(I) The percentage of students with GPA's between 2 and 2.5 is

CHOICE =

(II) The percentage of students with GPA's above 3.0 is:

PERCENTAGE =

(III) Above what GPA will the top 5% of the students be (i.e., compute the 95th percentile):

GPA =

(IV) If a sample of 25 students is taken, what is the probability that the sample mean GPA will be between 2.8 and 2.75?

CHOICE =

In a small town, there are 5 high school districts. Each district includes 100 high school

students. In total, there are 500 high school students in the town including 240 male

students and 260 female students. Researchers would like to select a sample of 200

students.

(a) Explain how the sample can be obtained using random cluster sampling.

(b) Explain how the sample can be obtained using stratified random sampling.

(c) Explain how the sample can be obtained using systematic random sampling.

. In 1973, the Basic Education Opportunity Grant (later renamed the Pell Grant) was established to provide grant aid to low-income students—not just recent high school graduates (“traditional students”) but also older students who might be returning to school (“nontraditional students”). The program was intended to increase college enrollment among the students most likely to face difficulties financing a college education. a. How is the effect of the Pell grant on college enrollment different for a student who is in his mid-20s than for a recent high school graduate?