Evaluate some background research on the various methods of linear and multiple regression techniques. Then discuss in scholarly detail using examples researched or based on life experiences how linear and multiple regression techniques are used to create data models to help organizations make decisions based on how these models output analyzed data.

Assume that the last two digits on a car number plate are equally likely to be any of the 100 outcomes{00, 01, 02, ........ 98, 99}. Peter bets Paul, at even money, that at least 2 of the next n cars seen will have the same last two digits. Does n=16 favour Peter or Paul? What value of n would make this a pretty fair bet?

Identify the independent and dependent variable:

question 1: a study was conducted to determine whether when a restaurant server drew a happy face on the check, that would increase the amount of tip.

question 2: a study was conducted to determine if the marital status of an individual had any effect on the cause of death of the individual.

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question 3: suggest some cofounding variables that the researcher might want to consider when doing a study

question 4: psychology today magazine reports that the more intelligent a person is (based on IQ,) the more willing the person is to make a cooperative choice rather than a selfish one.

eating 21 grams of fiber may help you lose weight.

1. A medical school claims that more than 28% of its students plan to go into general practice. It is found that among a random sample of 130 of the school's students, 32% of them plan to go into general practice. Find the P-value for a test of the school's claim

2. In a sample of 47 adults selected randomly from one town, it is found that 9 of them have been exposed to a particular strain of the flu. Find the P-value for a test of the claim that the proportion of all adults in the town that have been exposed to this strain of the flu is 8%.

3. An article in a journal reports that 34% of American fathers take no responsibility for child care. A researcher claims that the figure is higher for fathers in the town of Littleton. A random sample of 225 fathers from Littleton, yielded 97 who did not help with child care. Find the P-value for a test of the researcher's claim

4. An airline claims that the no-show rate for passengers booked on its flights is less than 6%. Of 380 randomly selected reservations, 18 were no-shows. Find the P-value for a test of the airline's claim.

5. Find the P-value for a test of the claim that less than 50% of the people following a particular diet will experience increased energy. Of 100 randomly selected subjects who followed the diet, 47 noticed an increase in their energy level

In Craps once the point is set, the shooter continues to roll the dice until either the point comes up (in which case the shooter wins) or a 7 comes up (in which case the shooter loses). At that time, the round ends.

• Suppose the point has just been set at 6. What is the probability that the round will end in 5 rolls or fewer (not including the come-out roll)?
• Suppose the point has just been set at 4. What is the probability that the round will end in 5 rolls or fewer (not including the come-out roll)?

Anystate Auto Insurance Company took a random sample of 376 insurance claims paid out during a 1-year period. The average claim paid was $1600. Assume σ = $262.

Find a 0.90 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

Find a 0.99 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

The length of industrial filters is a quality characteristic of interest. Thirty samples,each of size 5, are chosen from the process. The data yields an average length of

110 mm, with the process standard deviation estimated to be 4 mm.

(a) Find the warning limits for a control chart for the average length.

(b) Find the 3sigma control limits. What is the probability of a type I error?

(c) If the process mean shifts to 112 mm, what are the chances of detecting this shift

by the third sample drawn after the shift?

(d) What is the chance of detecting the shift for the first time on the second sample

point drawn after the shift?

(e) What is the ARL for a shift in the process mean to 112 mm? How many samples,

on average, would it take to detect a change in the process mean to 116 mm?

A newsgroup is interested in constructing a 90% confidence interval for the proportion of all americans who are in favor of a new green initiative. Of the 560 randomly selected Americans surveyed, 392 were in favor of the initiative.

a. With 90% confidence the proportion of all Americans who favor the new green initiative is between ___ and ___.

• Provide a definition of what makes a great leader. You must cite your resource.
• Identify someone you know who models this definition of leadership you have chosen.
  • Profile this person by describing this person’s abilities and traits that align with your definition of leadership.
  • Explain how this leader connects the definition and concepts of leadership with their workplace environment.
• Consider your own personal leadership skills and traits. Complete the Leadership Assessment Survey about yourself. Look at yourself as others might see you. Use a critical eye.
  • Summarize the results of your self-assessment.
• In conclusion, discuss the following points:
  • Why is it important to make the connection between leadership concepts and theory to workplace practices?
  • How do you apply leadership abilities and skills in your professional life?

• Authentic Leadership is the video on youtube by Vital worklife which should be seen before answering these questions.

Leadership Survey Form

Note: You do not submit this survey form for grading. You will summarize the results in your report.

Rate yourself on these 20 leadership traits and abilities. Be honest! Look at yourself with a critical eye.

The rating scale runs from 1 to 5.

1. Almost never     2. Seldom    3. Sometimes    4. Usually         5. Almost Always

a) Areas of greatest strengths:

b) Areas for development:

c) Overall evaluation:

2. I stand outside the student union and conduct a poll of passing students about their favorite fast food place. There are 6 response options = McDonald's, Wendy's, Burger King, Taco Bell, Popeye's, and Arby's. I also collect the student's year in school for demographic purposes - 5 levels - First Year, Sophomore, Junior, Senior, and Grad Student. I build a two-way table of this data to prepare to conduct a Chi-square analysis. How many degrees of freedom would my analysis have?

Group of answer choices:

6

35

20

5

1

3. The expected values for a Chi-Square Test of Independence come from:

Group of answer choices:

the population values

the marginals

a chi-square table

4. I conduct the Chi-Square test of independence for my Fast Food poll and obtain an observed Chi-square value of 22.55. The chisq-test() in R also reports a p-value of 0.3114. How do I interpret this result if my alpha is 0.05?

Group of answer choices

I fail to reject the null hypothesis and therefore determine that there is a significant association between fast food preference and class year.

I fail to reject the null hypothesis and therefore conclude that there is no association between class year and favorite fast food restaurant.

I reject the null hypothesis and conclude that there is a significant association between fast food preference and class year.

I reject the null hypothesis and conclude that there is no association between the variables fast food preference and class year.

5. My student union poll included another question regarding the preference for different dog breeds. I find a significant association between preferred dog breeds and gender of the students. I calculate a Cramer's V test and get a result of 0.05. What conclusion would I make about this result?

Group of answer choices:

The Cramer's V score disproves our statistical significant finding.

The Cramer's V value further proves that the result is significant.

The result was statistically significant, but not substantively significant.

6. I decide to conduct another poll outside the student union, and I want to ensure that my poll will have a low probability of Type II error and will be able to detect a difference with a large effect size. I run the following code:

pwr.chisq.test(w = 0.3, N=NULL, df = 20, sig.level = 0.05, power = 0.8)

I get the following output in R:

Chi squared power calculation

w = 0.3
N = 232.8977
df = 20
sig.level = 0.05
power = 0.8

What does this output tell me about how I need to design my next poll.

Group of answer choices

My new poll needs a power of 0.8 to have an effect size of 0.3.

A sample size of 230 should be sufficient for my poll.

Since I set my sample size at 233 I will achieve a power of 0.8.

I need a sample size of 233 students to obtain a result with the power I desire to have in my analysis.

7. The area under the curve of a normal distribution is equal to:

Group of answer choices

the mean of the distribution

a probability of 1.0

the standard deviation of the distribution.

the z-score

8. In my student union poll I asked students what they scored on the SAT. I know that the mean score of the UMD population is 1340 with a standard deviation of 222. My friend wants to know how her score of 1280 stacks up to the distribution of all scores at UMD.

What is her z-score?

Group of answer choices

-0.53

-1

0.27

-0.27

9. Another friend asked me to calculate his z-score so he could see how he compared to the distribution of SAT scores among UMD students. I found that his z-score was 0.33. What is the interpretation of his z-score?

Group of answer choices

He scored 3 SDs higher than the mean.

He scored better than 33% of students at UMD.

His SAT score shows he was 1/3 of an SD above the mean score.

He did worse than 33% of students at UMD.

10. We have more fitness test data from Vitor (who is male) and Manuela (who is female), who are applying to a military academy. Vitor did 50 push-ups in a minute, while Manuela only did 45.

We know that among previous applicants to the academy, the distribution of number of sit-ups is as follows:

Males have a mean of 60 and a standard deviation of 6.5.

Females have a mean of 40 and a standard deviation of 4.3.

What is the z-score for Manuela's result on the test?

Group of answer choices

1.16

1.69

-0.92

3.49

11. Vitor did 50 push-ups in a minute, while Manuela only did 45.

We know that among previous applicants to the academy, the distribution of number of sit-ups is as follows:

Males have a mean of 60 and a standard deviation of 6.5.

Females have a mean of 40 and a standard deviation of 4.3.

What is the z-score for Vitor's result on the test?

Group of answer choices:

0

2.33

-1.16

-1.54

12. Vitor did 50 push-ups in a minute, while Manuela only did 45.

We know that among previous applicants to the academy, the distribution of number of sit-ups is as follows:

Males have a mean of 60 and a standard deviation of 6.5.

Females have a mean of 40 and a standard deviation of 4.3.

Relative to their gender, who did better on the push-up test, Vitor or Manuela?

Group of answer choices:

Manuela

Vitor

State which sampling design should be used in the following situations, and justify your reasoning:

i. You need to collect statistics on types of software applications used by employees of a company. Separate lists of employees are available classified by job categories.

ii. Patients arriving at an emergency room facility are to be sampled to study their demographics, type of injury, etc. It is decided to sample 10% of the patients.

iii. An engineering school plans to conduct a mail survey of its alumni who graduated after 1980 to collect data on their current employment status. A complete alphabetical list of the alumni is available.

iv. A national sample of college students is to be taken, but a comprehensive list of all college students doesn't exist. A list of all colleges (private and public) exists. For any particular college, a list of all students can be obtained.

The following data have to do with the relationship between maternal smoking (# of cigarettes smoked per day,

which is variable X) and infant birth weight (which is variable Y). (∑X, ∑X², ∑Y, ∑Y², and ∑XY have already been

calculated for you and are shown below in red font.)

Cigarettes Per Day (X) X²    Infant Birth Weight (Y) Y² XY

2                                                        4                                            7.5                                 56.25                             15.0

6                                                      36                                            7.2                                 51.84                             43.2

10                                                100                                            6.9                                 47.61                             69.0

12                                                  144                                            6.2                                 38.44                             74.4

14                                                196    5.8 33.64 81.2

∑X = 44                                        ∑X² = 480                              ∑Y = 33.6                      ∑Y² = 227.78             ∑XY = 282.8

What is the y-intercept (a) for this data?

Suppose two independent random samples of sizes n1 = 9 and n2 = 7 that have been taken from two normally distributed populations having variances σ12 and σ22 give sample variances of s12 = 117 and s22 = 19. (a) Test H0: σ12 = σ22 versus Ha: σ12 ≠ σ22 with σ = .05. What do you conclude? (Round your answers to 2 decimal places.) F = F.025 = H0:σ12 = σ22 (b) Test H0: σ12 < σ22versus Ha: σ12 > σ22 with σ = .05. What do you conclude? (Round your answers to 2 decimal places.) F = F.05 = H0: σ12 < σ22

You are opening a doughnut franchise, but first, you must pass quality control on sugar glaze thickness before you can open. You randomly select 10 doughnuts from your production and send the following glaze thickness data to corporate headquarters for analysis: (units in mm)

1.21, 1.25, 1.23, 1.21, 1.28, 1.22, 1.27, 1.29, 1.20, 1.26

1. At α = 0.05, your sample data must statistically demonstrate that the mean glaze thickness is at least 1.20 mm. Determine whether or not your doughnuts meet this criterion.

1. Corporate also demands that the mean glaze thickness not by more than 0.025 inches. What sample size would you use in order to hold the probability of selling “bad” donuts to no more than 5%? Solve this problem analytically and graphically. (Hint: this is a β question)

Please solve by hand and not in Excel.