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)

Extra Practice / Homework 5) You are taking a multiple choice quiz which consists of 6 questions. Each question has five possible answers to choose from of which only one is correct. Answer the following questions a) What is your chance of choosing the correct answer for any particular problem? (express as a decimal rounded to two decimal places.) b) Explain how you could use your calculator to generate and use random numbers to simulate guessing on the each question of the quiz. c) Conduct a simulation with 20 trials indicating what random numbers were used and how many correct answers you got for each trial. d) Use your simulation to estimate for the probability of getting exactly one correct answer on the quiz if you guessed at all questions. e) Use your simulation to estimate for the probability of getting a score of less than 33.33% (fewer than 2 of 6 correct) on the quiz.

Trial Components Outcomes

Discuss the conceptual framework of PCA? What is its objective?

For all hypothesis testing problems Find each steps. Traditional method Step

1 State the null, alternative hypothesis, and identify the claim Step

2 Find the critical region and critical value(s) Step

3: Compute the test value Step

4 Make the decision to reject or do not reject H0 and conclusion.

Show how you arrived at your solution on the answer sheet for full credit. Write neatly, clearly and be organized.

1.The average hemoglobin reading for a sample of 20 teachers was 16 grams per 100 milliliters, with a sample standard deviation of 2 grams per 100 milliliters. (15 points)

a) Find the 99% confidence interval of the true mean.

b) Support the medical research team is investigating that true mean is 19 grams per 100 milliliters in a previous year, does your sample suggest that the true population mean for all teacher should be reject? Explain

c) Support the medical research team is investigating that true mean is 14 grams per 100 milliliters in a previous year, does your sample suggest that the true population mean for all teacher should be reject?

Explain 2. Of 318 randomly selected medical students, 21 said that they planned to work in a rural community. (15 points)

a) Find a 90% confidence interval for the true proportion of all medical students who plan to work in a rural community. Write your answer with three decimal places

b) If the population proportion is 0.037. Do you reject the population proportion? Explain

c) If the population proportion is 0.083. Do you reject the population proportion? Explain 3.

The manager of a large factory believes that the average hourly wage of the employees is below $9.98 per hour. A sample of 18 employees has a mean $9.60. the sample standard deviation is $1.42. At α = 0.10, is there enough evidence to support the manager’s claim? Use Traditional method (10 points)

4. A travel associate claim that the mean daily meal cost for two adults traveling together on vacation in New York is $105. A random sample of 20 such groups of adults has a mean daily meal cost of $110 and a sample standard deviation of $8.50. Is there enough evidence to reject the claim at α = 0.05? Use Traditional method (10 points)

5. Researchers suspect that 18% of all high school students smoke at least one pack of cigarettes a day. In New York one high school, with an enrollment of 300 students, a study found that 50 students smoked at least one pack of cigarettes a day. At α = 0.02, can the study conclude that 18% of all high school students smoke at least one pack of cigarettes a day? Use Traditional method (10 points)

6. A humane society claim that 35% of U.S. households own a cat. In a random sample of 300 U.S. households, 24% say they own a cat. At α = 0.02, is there enough evidence to reject the society’s claim? Use Traditional method (10 points)

Each of the following describes the outcome of a hypothetical bivariate correlational study. State whether you believe the correlation is a positive or negative one. With both the directionality problem and the third variable problem in mind, describe at least two ways of interpreting each.

There is a correlation between a student's college grades and the number of text messages sent per month.

The UDairy ice cream truck plans to sell ice cream at an upcoming alumni event in Central Park (NYC). From past events, demand for ice cream is highly weather dependent. On rainy days, demand is normally distributed with a mean of 120 scoops and standard deviation of 35 scoops. On non-rainy days, demand is normally distributed with a mean of 200 scoops and standard deviation of 60 scoops. The ice cream truck will be loaded two days before the event and travel to NYC. If the UDairy truck plans to bring enough ice cream to maintain a 90% service level for a rainy day, but the day surprisingly turns out to be non-rainy, what is the probability of the ice cream truck stocking out? For simplicity, assume the number of scoops demanded is a continuous variable. Enter probability as a three-digit decimal (e.g. 0.500, 0.275, 0.942).

Tully Tyres sells cheap imported tyres. The manager believes its profits are in decline. You have just been hired as an analyst by the manager of Tully Tyres to investigate the expected profit over the next 12 months based on current data.

•Monthly demand varies from 100 to 200 tyres – probabilities shown in the partial section of the spreadsheet below, but you have to insert formulas to ge the cumulative probability distribution which can be used in Excel with the VLOOKUP command.
•The average selling price per tyre follows a discrete uniform distribution ranging from $160 to $180 each. This means that it can take on equally likely integer values between $160 and $180 – more on this below.
•The average profit margin per tyre after covering variable costs follows a continuous uniform distribution between 20% and 30% of the selling price.
•Fixed costs per month are $2000.

(a)Using Excel set up a model to simulate the next 12 months to determine the expected average monthly profit for the year. You need to have loaded the Analysis Toolpak Add-In to your version of Excel. You must keep the data separate from the model. The model should show only formulas, no numbers whatsoever except for the month number.

The first random number (RN 1) is to simulate monthly demands for tyres.
•The average selling price follows a discrete uniform distribution and can be determined by the function =RANDBETWEEN(160,180) in this case. But of course you will not enter (160,180) but the data cell references where they are recorded.
•The second random number (RN 2) is used to help simulate the profit margin.
•The average profit margin follows a continuous uniform distribution ranging between 20% and 30% and can be determined by the formula =0.2+(0.3-0.2)*the second random number (RN 2). Again you do not enter 0.2 and 0.3 but the data cell references where they are located. Note that if the random number is high, say 1, then 0.3-0.2 becomes 1 and when added to 0.2 it becomes 0.3. If the random number is low, say 0, then 0.3-0.2 becomes zero and the profit margin becomes 0.2.
•Add the 12 monthly profit figures and then find the average monthly profit.

Show the data and the model in two printouts: (1) the results, and (2) the formulas. Both printouts must show the grid (ie., row and column numbers) and be copied from Excel and pasted into Word. See Spreadsheet Advice in Interact Resources for guidance.

(b)Provide the average monthly profit to Ajax Tyres over the 12-month period.

(c)You present your findings to the manager of Ajax Tyres. He thinks that with market forces he can increase the average selling price by $40 (ie from $200 to $220) without losing sales. However he does suggest that the profit margin would then increase from 22% to 32%.

He has suggested that you examine the effect of these changes and report the results to him. Change the data accordingly in your model to make the changes and paste the output in your Word answer then write a report to the manager explaining your conclusions with respect to his suggestions. Also mention any reservations you might have about the change in selling prices.

The report must be dated, addressed to the Manager and signed off by you.
(Word limit: No more than 150 words)

My factory makes thermometers and I am testing if they are accurate. I will test this by measuring the average temperatures of different thermometers in ice-water. The null hypothesis is that the true average reading of thermometers from this factory in ice-water is 0◦ against the two-sided alternative. I will construct a p-value. What will the value of the p-value mean? If you wish, you can pretend the value of the p-value will be 0.06.

Parking lots; A survey of autos parked in student and staff lots at a large university classified the brands by country of origin, as seen in the table

                               Driver

                       Student      Staff

American         104            105

European         33               11

Asian                55               48

a) What percentage of all cars surveyed wcre American?

b) What percentage of the American cars were owned by students?

c) What percen of the students owned American

d) What is the marginal distribution of origin ?

e) What is the condition of drivers American cars?

f) Do you think that the origin of the car is independent of the type of driver? Explain

A population proportion is 0.5. A sample of size 200 will be taken and the sample proportion will be used to estimate the population proportion. Use z-table.

Round your answers to four decimal places. Do not round intermediate calculations.

a. What is the probability that the sample proportion will be within +/-0.02 of the population proportion?

b. What is the probability that the sample proportion will be within +/-0.07 of the population proportion?

1. Using the 50-35-14-2 rule, sketch each of the distributions above.

2. For each variable, calculate the value of X at the 40^th %ile and the 61^nd %ile.

3. For each variable, calculate the %ile corresponding to a score of 4 on the variable.

4. 2013 SAT subscores for the nation are given below.

A) For the composite, what score do you need to qualify for Mensa, which requires you to be in the top 2% of the population?

B) Oddly enough, Phillip scored exactly 500 on each subscore… what percent of students scored higher in each subscore? What percent of students scored LOWER than his composite score of 1000?

C) MU admissions accept a 1080 composite score as sufficient to demonstrate potential success as a student. What percent of students qualify?

D) The MU honor’s college accepts incoming freshmen with a composite SAT of 1380 (if you were ALSO top 15%ile of high school class). What percent of students qualify with that composite score?