Ada Nixon, a student, has just begun a 30-question, multiple-choice exam. For each question, there is exactly one correct answer out of four possible choices. Unfortunately, Ada hasn't prepared well for this exam and has decided to randomly select an answer choice for each question.

(a) (4 points) For a given question, what is the probability Ada picks the correct answer, assuming each answer choice is equally likely to be selected?

(b) Assume the number of questions Ada answers correctly is Binomially distributed.

i. (4 points) What is the average number of questions Ada will answer correctly? Show your work and round your nal answer to 1 decimal place.

ii. (3 points) If Ada answers at least 16 questions correctly, she will receive a passing grade. What is the probability that Ada receives a passing grade? Show your work, including any calculator functions you use, and round your nal answer to 3 decimal places.

(c) (3 points) Suppose Ada comes across a question for which she knows two of the answer choices are certainly wrong, which means the correct answer must be one of the two remaining choices. Assuming Ada will answer every other question using the same random selection procedure as before, will the number of questions she answers correctly remain binomially distributed? State Yes or No and explain why

A random sample is drawn from a normally distributed population with mean μ = 19 and standard deviation σ = 1.8. [You may find it useful to reference the z table.]

a. Are the sampling distribution of the sample mean with n = 27 and n = 54 normally distributed?

Yes, both the sample means will have a normal distribution.

No, both the sample means will not have a normal distribution.

No, only the sample mean with n = 27 will have a normal distribution.

No, only the sample mean with n = 54 will have a normal distribution.

b. Calculate the probabilities that the sample mean is less than 19.9 for both sample sizes. (Round intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

A fun size bag of M&Ms has 4 blue, 3 orange, 3 red, 2 green, 2 yellow, and 1 brown M&Ms. What is the probability of randomly selecting 5 M&Ms where 3 are blue and 2 are orange?

Flair Furniture Company produces inexpensive tables and chairs. The production process for each is similar in that both require a certain number of labor hours in the carpentry department and a certain number of labor hours in the painting department. Each table takes 3 hours of carpentry work, an hour and a half of assembly and 2 hours of finishing work. Each chair requires 4 hours of carpentry, and hour and 15 minutes of assembly and 1 hour of painting. During the current month, 2,400 hours of carpentry time, 800 hours of assembly time and 1,000 hours of painting time are available. Each table sold results in a profit contribution of $7, and each chair sold yields a profit contribution of $5.

a. Set up a Solver model for determine the number of tables and chairs to produce that will maximize total profit contribution. Run Solver and generate the Answer Report and Sensitivity Report.

b. Identify the binding and nonbinding constraints and explain what it means.

c. Construct the sensitivity range for the objective function coefficients. Give an interpretation for each range.

d. Construct the sensitivity range for the right hand side coefficient of constraints. Give an interpretation for each range and the corresponding shadow price of all the constraints.

e. Suppose that 100 hours of additional labor can be added. In which department would you add these hours? Explain why. How much additional profit can be generated by this addition?

3) A tax auditor has a pile of federal tax returns and she has been directed to randomly select 20 of these returns for a special audit. Describe how systematic sampling could be used. 4) A recent radio station asked listeners to go to their website and vote for their favorite singing star. A responder would be randomly chosen and would receive two tickets to the performance of their choice. What type of sampling is used for the vote? 5) A community college is selected at random from all US community colleges and the GPAs and ages of all students from that college are examined. a) What type of sampling was done? b) What is the population of interest for this study? c) If the average GPA is computed for this sample would it be considered a statistic or a parameter? d) Suppose instead the researchers wanted to implement a Simple Random Sample of community college students, how might they do this? 6) Explain the difference between cluster sampling and stratified sampling.

the music on a music player can be stored digitally in several formats. a popular format for a digital music player is aiffshort for Audio Interchange File Format. Another format is known as​ AAC, short for Advanced Audio Coding. Files on a digital music player can be in either of these formats or both. The 25 songs in this data set use a mixture of these two formats. Complete parts​ (a) through​ (d) below. Create a dummy variable using the arc format as the baseline category to represent the format of the song in the data file and then fit the regression model for how much space is needed to store a song based on the length of a song. write down the regression model including the estimates of the intercepts

Sheila's measured glucose level one hour after a sugary drink varies according to the Normal distribution with μμ = 130 mg/dl and σσ = 15 mg/dl. What is the level L such that there is probability only 0.15 that the mean glucose level of 4 test results falls above L?

L=

A study of the career paths of hotel general managers sent questionnaires to an SRS of 210 hotels belonging to major U.S. hotel chains. There were 88 responses. The average time these 88 general managers had spent with their current company was 12.7 years. (Take it as known that the standard deviation of time with the company for all general managers is 3.6 years.)

(a) Find the margin of error for an 85% confidence interval to estimate the mean time a general manager had spent with their current company:  years

(b) Find the margin of error for a 99% confidence interval to estimate the mean time a general manager had spent with their current company:  years

(c) In general, increasing the confidence level  the margin of error (width) of the confidence interval. (Enter: ''DECREASES'', ''DOES NOT CHANGE'' or ''INCREASES'', without the quotes.)

Use SPSS for this Application Exercise:
A staff psychologist at a police precinct believes that the new week-long training courses worsens on the job sensitivity of police officers. The psychologist designs a study where some policemen randomly get and complete the course. A month later the psychologist records the number of domestic disputes the police officers successfully resolved from their police reports. What can the psychologist conclude with α = 0.05. The success data are below.

a) What is the appropriate test statistic?
---Select--- na z-test One-Sample t-test Independent-Samples t-test Related-Samples t-test

b)
Condition 1:
---Select--- job sensitivity no course completing the course police precinct domestic disputes
Condition 2:
---Select--- job sensitivity no course completing the course police precinct domestic disputes

c) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
p-value =  ; Decision:  ---Select--- Reject H0 Fail to reject H0

d) Using the SPSS results, compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
d =  ;   ---Select--- na trivial effect small effect medium effect large effect
r² =  ;   ---Select--- na trivial effect small effect medium effect large effect

e) Make an interpretation based on the results.

Participants that received training had significantly less resolved domestic disputes than those that did not receive training.

Participants that received training had significantly more resolved domestic disputes than those that did not receive training.    

Participants that received training did not differ significantly on resolved domestic disputes than those that did not receive training.

1. Have you ever purchased an article of clothing (dress, sports jacket, etc.), worn the item once to a party, and then returned the purchase? This is called a one-time fling. About 10% of all adults deliberately do a one-time fling and fell no guilt about it. In a group of seven adult friends, what is the probability that:
   1. No one has done a one-time flng?
   2. At least one person has done a one-time flng?
   3. No more than two people have done a one-time fling?
   4. What is the average number (expected value) of people who have done a one-time fling?
   5. What is the standard deviation

4. What is the difference between the null and alternative hypotheses? What does alpha

      represent? (4 pts)

The proportion of professional baseball players who take steroids has been assumed to be twenty percent by the team owner council. The Commissioner of Baseball has instituted a new campaign to reduce the proportion of players who take steroids. The Commissioner would now like to test whether their campaign has worked. (α = 0.05)

      State the null and alternative hypotheses that the Commissioner would test. Use

      symbols in the hypotheses. State alpha and define the parameter. (7 pts)

Ho: p = 0.2 (.)       

      Ha: p < 0.2 (.)                                

Time Magazine states that the nationwide drop out rate for high school seniors is ten percent. You conduct a test to see if the drop out rate for high school seniors is actually more than ten percent. ( α = 0.01)

     State the null and alternative hypotheses for this test. Use symbols in the hypotheses.

     State alpha and define the parameter. (7 pts)

The Maryland Department of Health claims that the proportion of heroin users in Maryland that have been infected by HIV is four percent. Suppose a researcher wants to show that this claim is not true. ( α = 0.1)

     State the null and alternative hypotheses to dispute the Maryland Department of

     Health’s claim. Use symbols in the hypotheses. State alpha and define the parameter.

    (7 pts)

Ho:        

      Ha:

1) (from Samuels and Witmer, 2003) If you walk toward a squirrel that is on the ground, it will eventually run to the nearest tree for safety. A researcher wondered whether he could get closer to the squirrel than the squirrel was to the nearest tree before the squirrel would start to run. Thus, for each studied squirrel he recorded the distance from person-to-squirrel and the distance from squirrel-to-tree, at the moment when the squirrel started to run. The measurements are in the txt file on the web. Conduct statistical test to determine if there is a difference between person-to-squirrel and squirrel-to-tree distances (use α=0.05). For the test do the following:

a) Explain whether you will do a test for independent samples or a test for paired samples.

b) Explain whether you will do a 1-tailed or a 2-tailed test.

c) What is the assumption for this statistical test? Is it met?

Show 2 different indicators that you used for checking assumptions (you can do this part in either SAS or R and show only the outputs from either SAS or R). Comment on what each indicator tells you about the assumption.

d)     Conduct the test you decided on in parts a) and b) by hand. Show:
Null hypothesis:
Research Hypothesis:
Value of Test Statistic:
Critical Value:
Conclusion:

e)     Use SAS and R to conduct the test you decided on in parts a) and b)

What is the p-value for your test?

Explain how you used p-value to reach conclusion.

squirrelID TypeOfDistance y

1 fromPerson 81
2 fromPerson 178
3 fromPerson 202
4 fromPerson 325
5 fromPerson 238
6 fromPerson 120
7 fromPerson 240
8 fromPerson 326
9 fromPerson 60
10 fromPerson 119
11 fromPerson 189
12 fromPerson 79
13 fromPerson 180
14 fromPerson 200
15 fromPerson 330
16 fromPerson 240
17 fromPerson 132
18 fromPerson 242
19 fromPerson 328
20 fromPerson 55
21 fromPerson 121
1 fromTree 137
2 fromTree 34
3 fromTree 51
4 fromTree 150
5 fromTree 54
6 fromTree 236
7 fromTree 45
8 fromTree 293
9 fromTree 277
10 fromTree 83
11 fromTree 81
12 fromTree 47
13 fromTree 233
14 fromTree 42
15 fromTree 31
16 fromTree 290
17 fromTree 51
18 fromTree 48
19 fromTree 80
20 fromTree 274
21 fromTree 134

. Identify the independent variable, dependent variable and direction of the hypotheses.

a)         The higher the income, the less likely a person will vote Republican.

b)         The more often a student attends class, the higher the student’s score on the final exam.

c)         The smaller the automobile’s engine, the higher the automobile’s gas mileage.

d)         If an undergraduate student visits an advisor for course scheduling, the more likely the

            student will graduate within four years.

e)         The more spinach a person consumes, the lower the person’s total cholesterol.

A particular book publisher is thinking about starting up a new national magazine in a small town. It's thought that this publisher would have to get over 12% of the book market to be financially secure. While planning to launch this magazine, a survey was taken of a sample of 400 readers. After providing an inside look into this magazine, one question asked the participants if they would subscribe to this magazine if the cost didn't exceed $20 per month. Suppose that the number of participants that said they would subscribe is 58.

a. Can this publisher conclude that this proposed magazine will be financially feasible?

b. Suppose that the true value of the overall proportion of readers who will subscribe to this magazine is .13. Was the decision made in part a correct? If not, what type of error was made?

c. State the meaning of a type 1 and type 2 error in the content of this example. What would be the consequences of making these errors to the publisher?

A researcher was interested in the effects of caffeine on sleep. She measured how many minutes it took for ten participants to fall asleep. Half of the participants drank a liter of caffeinated soda before going to sleep while the other half were only allowed to drink water. Summary data of minutes are presented below. Did the caffeine increase the length of time it took to fall asleep (a =.05)?

         Water Group Caffeine Group

                     18 22

                     15 15

                     19 20

                     14 21

                     14 19

a. Name the test to be conducted and why you selected it:

b. State the null and alternative hypotheses:

c. State the CV and the decision rule. Sketch the rejection region:

d. In addition, calculate the value of eta2 (h2).

e. Write out an APA style conclusion based on this finding:

Writing Assignment #1 Instructions
The following assignment should be typed and printed or handwritten and turned in to the CA office in room​ 201 TMCB.​ If there is no one in the CA Office, you can slip your assignment through the slot in the door.
You must follow the instructions below or you will not receive credit.​ You can turn in the assignment up until 5:00 PM on the due date.
Important Notices: If you do not staple multiple pages, you may lose points. If you do not put your section number on the paper, you may lose points. As shown below, please fold your paper lengthwise and on the outside write (a) your name, (b) Stat 121, (c) your section number, and (d) the assignment number. (An example is available outside the CA Office.)
The situation is as follows:
Rent and other associated housing costs, such as utilities, are an important part of the estimated costs of attendance at college. A group of researchers at the BYU Off-Campus Housing department want to estimate the mean monthly rent that unmarried BYU students paid during Winter 2019. During March 2019, they randomly sampled 366 BYU students and found that on average, students paid $348 for rent with a standard deviation of $76. The plot of the sample data showed no extreme skewness or outliers.

Calculate a 98% confidence interval estimate for the mean monthly rent of all unmarried BYU students in Winter 2019.
STATE
What is a 98% confidence interval estimate for the mean monthly rent of all unmarried BYU students in Winter 2019?
PLAN
1. State the name of the appropriate estimation procedure. ​(2pts)
2. Describe the parameter of interest in the context of the problem. ​(2pts)
SOLVE
1. Name the conditions for the procedure. ​(2pts)
2. Explain how the above conditions are met. ​(2pts)
3. Write down the confidence level and the t* critical value. ​(2pts)
4. Calculate the margin of error for the interval to ​two decimal places​. ​Show your work. ​(2pts)
5. ​Calculate the confidence interval ​to two decimal places​ and state it ​in interval form​. ​(2pts)
CONCLUDE
Interpret your confidence interval in context. Do this by including these three parts in your conclusion ​(3 pts)​:
● Level of confidence​ (1pt)
● Parameter of interest in context ​(1 pt)
● The interval estimate ​(1 pt)
FURTHER ANALYSIS
1. How would selecting a 95% level of confidence change the size of the calculated confidence interval? (1pt). Explain or justify your answer by recalculating (1pt) .

2. At a 95% level of confidence, what sample size would be needed to estimate the parameter of interest to within a margin of error of ± $25? Use σ = $76. ​(2pts)
3. Suppose that a second random sample of unmarried BYU students was conducted during March 2019. Using this data, the confidence interval was calculated to be ​($342.67, $349.35)​. ​Rounded to two decimal places​, what is the margin of error for this confidence interval? Show your work. (1pt)