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Stats Extra Credit Assignment, Exams of Advanced Education

Walden University Advanced Education

An extra credit assignment for a statistics course at santa fe college. It covers various statistical concepts such as sampling, experimental design, probability, and random variables. Detailed questions and problems for the students to solve, which could serve as a valuable study guide for an upcoming test. The assignment covers a wide range of topics, including identifying population and sample characteristics, calculating probabilities, and analyzing random variables. By working through these problems, students can deepen their understanding of the statistical principles and techniques covered in the course, and prepare themselves for the upcoming exam.

Typology: Exams

2024/2025

Available from 10/03/2024

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STA 2023: Stats extra credit #2 Santa Fe College

Type only the answers. When you are finished, upload your completed document in Canvas.

I will post a blank copy and solutions after the due date.

This extra credit assignment is a great study guide for the test.

Give your answers as exact fractions or round to 4 decimal places.

1. Researchers, hoping to determine the percentage of U.S. college students who believe in ghosts, went to Santa Fe

College to conduct a survey. Random samples of 20 students were taken from each major field of study (ie 20

Mathematics majors, 20 English majors, …) and were asked whether or not they believed in ghosts.

Identify the following:

a. The population- U.S college students

b. The population parameter of interest- The percentage of U.S college students who believe in ghosts.

c. The sample- 20 students from each major field of study from Santa Fe College.

d. The sampling method (SRS, stratified, cluster, or systematic)- Cluster

e. Any potential sources of bias you can detect and any problems you see in generalizing to the population

of interest The sample of Santa Fe students drawn from the survey portrays that there might be a

convenience sample since we are only gathering students in one county, while in effort to describe a

whole country. (United States)

2. Scientists at a major pharmaceutical firm investigated the effectiveness of 3 herbal compounds (compound A,

compound B, and compound C) to treat obesity. 40 volunteers suffering from obesity participated. Subjects were

randomly assigned to one of the compounds or to a sugar solution known to have no effect. After 2 months,

scientists compared the average difference in weight among the different groups.

Identify:

a. The subjects studied Obesity/ retrospective study

b. The factor(s) in the experiment and the number of levels of each

Factors: 3 herbal compounds

Levels: 4 (Compound A, B, C, and placebo (sugar solution))

c. The number of treatments 4

d. The response variable measured weight average

e. The design (completely randomized, blocked, or matched pairs) completely randomized

f. Whether it was blinded or not- Blinded

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STA 2023: Stats extra credit # 2 Santa Fe College

Type only the answers. When you are finished, upload your completed document in Canvas. I will post a blank copy and solutions after the due date. This extra credit assignment is a great study guide for the test. Give your answers as exact fractions or round to 4 decimal places.

Researchers, hoping to determine the percentage of U.S. college students who believe in ghosts, went to Santa Fe College to conduct a survey. Random samples of 20 students were taken from each major field of study (ie 20 Mathematics majors, 20 English majors, …) and were asked whether or not they believed in ghosts. Identify the following:

a. The population- U.S college students

b. The population parameter of interest- The percentage of U.S college students who believe in ghosts.

c. The sample- 20 students from each major field of study from Santa Fe College.

d. The sampling method (SRS, stratified, cluster, or systematic)- Cluster

e. Any potential sources of bias you can detect and any problems you see in generalizing to the population of interest The sample of Santa Fe students drawn from the survey portrays that there might be a convenience sample since we are only gathering students in one county, while in effort to describe a whole country. (United States)

2. Scientists at a major pharmaceutical firm investigated the effectiveness of 3 herbal compounds (compound A, compound B, and compound C) to treat obesity. 40 volunteers suffering from obesity participated. Subjects were randomly assigned to one of the compounds or to a sugar solution known to have no effect. After 2 months, scientists compared the average difference in weight among the different groups. Identify:

a. The subjects studied Obesity/ retrospective study

b. The factor(s) in the experiment and the number of levels of each Factors: 3 herbal compounds Levels: 4 (Compound A, B, C, and placebo (sugar solution))

c. The number of treatments 4

d. The response variable measured weight average

e. The design (completely randomized, blocked, or matched pairs) completely randomized

f. Whether it was blinded or not- Blinded

Sample Spaces – list the sample spaces

a. Toss 2 coins one at a time and record the order of heads and tails. SS= {HH, TT, TH, HT}

b. Toss a coin and then a die. SS= {H,T} and SS= {1,2,3,4,5,6}

c. Toss four coins and record the number of tails. SS= {1,2,3,4}

Round All probabilities to 4 decimal places

a. P(all hearts) =.

b. P(no queens) =.

c. P(at least one heart) =.

d. P(the 2nd^ card is the only heart) = 0.

7. Real estate ads suggest that 60% of homes for sale have garages, 20% have swimming pools, and 15%

have both. What is the probability that a home for sale has

a. A pool or a garage? = 0.

b. A pool but no garage? =.

c. Neither a pool nor a garage? =.

d. If it is known that a home for sale has a pool, what is the probability that it has a garage?

Random Variables Game- Pick a card from a standard 52 card deck Cost to play - $3. If you choose a Red , you get nothing. If you choose a ♣, you get $3.00. If you choose a ♠ you get $5.00. If you choose the Ace of ♠, you get an additional $20.00.

a. Create a probability model for the players resulting amount after 1 play. (just fill out the table)

Outcome x P(X = x ) Red - 3 26/ Club 0 13/ Spade 2 13/52 but if we are count the ace of spades in its own group we would have 12/ Ace of Spade 17 1/

b. What does the random variable represent? X = Amount end up with after the one play at this game

c. Find the player’s expected resulting amount after 1 play. = $-0.

d. Find the standard deviation. = $3.

e. Who has the advantage, the player or the person holding the game? The person holding the game has the advantage.

Let X and Y be two independent random variables with the following means and standard deviations.

Mea n

Standard Deviatio n X 80 15 Y 65 8

Find the following.

a. The mean of 3X. = 240

b. The standard deviation of Y+10. =12.

c. The mean of X+Y. =

d. The standard deviation of X + Y. = 17