Question

In: Statistics and Probability

If you have 80 students in an introductory biology statistics class and only 70 are biology...

If you have 80 students in an introductory biology statistics class and only 70 are
biology students, then:
(a) Compare the probabilities that you will get no biology students in a random
sample of size 6 when you sample with and without replacement.
(b) Compare the probabilities that you will get all biology students in a random
sample of size 6 when you sample with and without replacement.
(c) Compare the probabilities that you will get 14 biology students and 2 non-
biology students in a sample of size 16 when you sample with and without
replacement.

Solutions

Expert Solution

Total number of students = 80

Number of Biology students = 70

Number of non-Biology students = 80-70=10

a) Sample with replacement. For each selection the number of non-biology students remain at 10 and the total students remain at 80

Number of ways of selecting 6 non-biology students from 10 is

Total number of ways of selecting 6 students from 80 is

the probabilities that you will get no biology students in a random sample of size 6 is same as

the probability that you select 6 non-biology students in a random sample of size 6

ans: the probabilities that you will get no biology students in a random sample of size 6, when you sample with replacement, is 0.0000038

Sample without replacement.

Number of ways of selecting 6 non-biology students from 10 is

Total number of ways of selecting 6 students from 80 is

the probability that you will get no biology students in a random sample of size 6 is same as

the probability that you select 6 non-biology students in a random sample of size 6

ans: the probability that you will get no biology students in a random sample of size 6, when you sample without replacement, is 0.00000070

b) Sample with replacement. For each selection the number of biology students remain at 70 and the total students remain at 80

Number of ways of selecting 6 biology students from 70 is

Total number of ways of selecting 6 students from 80 is

the probability that you will get all biology students in a random sample of size 6 is same as

the probability that you select 6 biology students in a random sample of size 6

ans: the probability that you will get all biology students in a random sample of size 6, when you sample with replacement, is 0.4488

Sample without replacement.

Number of ways of selecting 6 biology students from 70 is

Total number of ways of selecting 6 students from 80 is

the probability that you will get all biology students in a random sample of size 6 is same as

the probability that you select 6 biology students in a random sample of size 6

ans: the probability that you will get all biology students in a random sample of size 6, when you sample without replacement, is 0.4363

c) Sample with replacement. For each selection the number of biology students remain at 70 and the total students remain at 80

Number of ways of selecting 14 biology students from 70 and 2 non-biology from 10 is

But we can arrange these 14 biology and 2 non-biology in

ways

Number of ways of selecting and arrange 14 biology students from 70 and 2 non-biology from 10 is

Total number of ways of selecting 16 students from 80 is

the probabilities that you will get 14 biology students and 2 non-biology students in a sample of size 16 is

ans: the probabilities that you will get 14 biology students and 2 non-biology students in a sample of size 16 , when you sample with replacement, is 0.2891

Sample without replacement.

Number of ways of selecting 14 biology students from 70 and 2 non-biology from 10 is

Total number of ways of selecting 16 students from 80 is

the probabilities that you will get 14 biology students and 2 non-biology students in a sample of size 16 is

ans: the probabilities that you will get 14 biology students and 2 non-biology students in a sample of size 16, when you sample without replacement, is 0.3226

orchestra answered 1 year ago

Next > < Previous

Related Solutions

The introductory biology class at a large university is taught to hundreds of students each semester....

The introductory biology class at a large university is taught to hundreds of students each semester. For planning purposes, the instructor wants to find out the average amount of time that students would use to take the first quiz if they could have as long as necessary to take it. She takes a random sample of 100 students from this population and finds that their average time for taking the quiz is 20 minutes, and the standard deviation is 10...

In a large class of introductory Statistics students, the professor has each person toss a coin...

In a large class of introductory Statistics students, the professor has each person toss a coin 29 times and calculate the proportion of his or her tosses that were heads. Complete parts a through d below. The Independence Assumption (is or is not) )_____satisfied because the sample proportions (are or are not)_____independent of each other since one sample proportion (can affect or does not affect)______another sample proportion. TheSuccess/Failure Condition is not satisfied because np=____ and nq=____which are both (less than...

COIN TOSSES In a large class of introductory Statistics students, the professor has each student toss...

COIN TOSSES In a large class of introductory Statistics students, the professor has each student toss a coin 16 times and calculate the proportion of his or her tosses that were heads. The students then report their results, and the professor plots a histogram of these several proportions. What shape would you expect this histogram to be? Why? Where do you expect the histogram to be centred? How much variability would you expect among these proportions? Explain why a Normal...

A professor who teaches a large introductory statistics class (197 students) with eight discussion sections would...

A professor who teaches a large introductory statistics class (197 students) with eight discussion sections would like to test if student performance differs by discussion section, where each discussion section has a different teaching assistant. The summary table below shows the average score for each discussion section as well as the standard deviation of scores and the number of students in each section. Sec 1 Sec 2 Sec 3 Sec 4 Sec 5 Sec 6 Sec 7 Sec 8 ni...

Below are the final exam scores of 20 Introductory Statistics students.

Below are the final exam scores of 20 Introductory Statistics students. Student 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Score 71 76 77 77 79 80 80 80 81 81 84 84 85 86 86 86 86 87 89 93 The mean exam score is 82.4 with a standard deviation of 5.14. 1. How many of the exam scores in the sample are within one standard deviation...

Students in a biology class have been randomly assigned to one of the two mentors for...

Students in a biology class have been randomly assigned to one of the two mentors for the laboratory portion of the class. A random sample of final examination scores has been selected from students supervised by each mentor, with the following results: Mentor A: 78, 78, 71, 89, 80, 93, 73, 76 Mentor B: 74, 81, 65, 73, 80, 63, 71, 64, 50, 80 At the 0.05 significance level, is there a difference in the mean scores?

A statistics class for engineers consists of 53 students. The students in the class are classified...

A statistics class for engineers consists of 53 students. The students in the class are classified based on their college major and sex as shown in the following contingency table: College Major Sex Industrial Engineering Mechanical Engineering Electrical Engineering Civil Engineering Total Male 15 6 7 2 30 Female 10 4 3 6 23 Total 25 10 10 8 53 If a student is selected at random from the class by the instructor to answer a question, find the following...

A: You recently took a statistics class in a large class with n = 500 students....

A: You recently took a statistics class in a large class with n = 500 students. The instructor tells the class that the scores were Normally distributed, with a mean of 7 2 (out of 100 ) and a standard deviation of 8 , but when you talk to other students in the class, you find out that more than 30 students have scores below 45 . That violates which rule for the Normal distribution? the 30–60–90 rule the 1–2–3...

A professor of a introductory statistics class has stated that, historically, the distribution of final exam...

A professor of a introductory statistics class has stated that, historically, the distribution of final exam grades in the course resemble a normal distribution with a mean final exam mark of 60% and a standard deviation of 9%. (a) What is the probability that a randomly chosen final exam mark in this course will be at least 75%? (b) In order to pass this course, a student must have a final exam mark of at least 50%. What proportion of...

A student survey was completed by 446 students in introductory statistics courses at a large university...

A student survey was completed by 446 students in introductory statistics courses at a large university in the fall of 2003. Students were asked to pick their favorite color from black, blue, green, orange, pink, purple, red, yellow. (a) If colors were equally popular, what proportion of students would choose each color? (Round your answer to three decimal places.) (b) We might well suspect that the color yellow will be less popular than others. Using software to access the survey...

Subjects