Consider a population that consists of the 70 students enrolled in a statistics course at a large university. If the university registrar were to compile the grade point averages (GPAs) of all 70 students in the course and compute their average, the result would be a mean GPA of 2.98. Note that this average is unknown to anyone; to collect the GPA information would violate the confidentiality of the students’ academic records.

Suppose that the professor who teaches the course wants to know the mean GPA of the students enrolled in her course. She selects a sample of students who are in attendance on the third day of class. The GPAs of the students in the sample are:

1) The instructor uses the sample average as an estimate of the mean GPA of her students. The absolute value of the error in the instructor’s estimate is:

a) 0.52

b) 0.62

c) 0.86

d) 0.80

The portion of this error that is due to errors in data acquisition, nonresponse bias, and selection bias is referred to as 2) non sampling error/sampling error. This type of error is 3) more/less serious than 4) non sampling error/sampling error because taking a larger sample 5) will diminish/will not diminish its size or possibility of occurrence.

Suppose students in the university’s honors program are on a field trip on the third day of class. This may have introduced an 6) error in data acquisition/selection bias/a non response error/sampling error . Correcting this error will 7) sometimes/always/never bring the sample closer to the true mean GPA.

Suppose that the instructor incorrectly recorded the value 3.74 in the data and that the correct value is 3.47. This contribution to the error was caused by 8) error in data acquisition/selection bias/a non response error/sampling error. Given the instructor’s sample, correcting this error would bring the sample mean 9) Closer to the true mean GPA/Farther from the true mean GPA/To the exact value of the true mean GPA.

Suppose a student who was selected for the sample declines to disclose her GPA. This may have introduced 10) error in data acquisition/selection bias/a non response error/sampling error. Correcting this error will 11) sometimes/always/never bring the sample closer to the true mean GPA.

The professor suspects that her sample is flawed. She assigns each of the students in the class an ID number from 1 to 70 and uses Excel to select a simple random sample of ID numbers. The professor meets with the students in the sample. Each student signs a release that gives the registrar permission to use the student’s GPA to compute the sample average. The professor assures the students that the registrar will provide her with the average and not the GPAs of individual students.

The GPAs of the students in the new sample (from their academic records held by the registrar) are:

12) The professor uses the new sample average provided by the registrar as an estimate of the mean GPA of the students in the course. The absolute value of the error in her estimate is:

a) 0.42

b) 0.26

c) 0.01

d) 0.55

This error is 13) non sampling error/sampling error , and the only way to reduce its expected size is to 14) increase/decrease the sample size.

In this discussion board assignment, you will critically evaluate the following scenario using the four basic critical questions. Here is the scenario:

Researchers wanted to study the relationship between pizza consumption by college freshmen and academic achievement. The researchers selected a freshmen history class with 900 students. The class lasted for 16 weeks and had weekly quizzes.

The researchers used random sampling and got two equivalent groups of participants from the class. Each group had 35 students. One group was the pizza group and one was the non-pizza group. To prepare for the experiment, the researchers compared the average quiz results of both groups for the first three weeks of the course and found no statistically significant difference between quiz scores.

In weeks 4 - 12, the researchers provided pizza dinner for everyone in the pizza group but those in the non-pizza group were told not to eat pizza 48 hours before the weekly quizzes. After week 12, the researchers compared the average quiz scores in each group and found that the non-pizza group had a statistically higher average quiz score than the pizza group. The researchers concluded that pizza consumption hinders academic performance of college freshmen.

Here are the basic 4 critical questions:

The next step to critically evaluate correlational claims is asking our four basic CRITICAL QUESTIONS applied to correlation (p. 118):

What does the claim of correlation mean? Which two variables, changing events, factors, or things co-vary? Do they exhibit a positive or negative relation?

How good is the evidence? Are two relevant groups being compared? Is the difference between the groups large enough (i.e., outside the margin of error of both samples) so that it is unlikely that these differences are the result of chance sampling variation? Were the groups being compared appropriately selected?

What other information is relevant? What is the context? Have other researchers found similar correlations? Of similar strength? Did other researchers use different types of samples and groups?

Are relevant fallacies avoided? For example, consider the fallacies of No comparison, Biased Sampling, Small Sample, Unclear Target Population, and of Significance.

These fallacies are clearly described in our textbook. Since most have been already covered in the previous chapters of our textbook, corresponding online links, and in the Keynotes, we need only introduce the new fallacy of Significance. The error of reasoning here for this fallacy is to argue that the difference between two (sample) groups, in a strict statistical or scientific sense, is important—relying on the common usage of the word “significant.” In contrast, the “[d]ifferences are said to be ‘statistically significant’ when…we can theoretically be 95% confident that the differences are not due to chance” (according to what we learned about statistical reasoning in Chapter 3 of our textbook; p. 105, emphasis added). This, therefore, merely provides a probabilistic judgement about a result that is basically not significant or important in any ordinary sense. As Mark Battersby notes, “[a] ‘statistically significant difference’ between two groups means that it’s very likely that there’s a correlation; but this says nothing about the strength of the correlation or about whether the correlation is of any human, scientific, or personal significance” (pp. 114-115, emphasis added).

Kim is a 27-year-old woman who recently moved from a small

town in Texas to work in the city of Dallas as a reporter for one

of the major newspapers. She is 5’6” tall and weighs 115 lb. To

keep in shape she likes to jog, which she did regularly in her

hometown. She doesn’t know anyone in Dallas and has been

lonely for her family since arriving. But she has moved into a

small apartment in a quiet neighborhood and hopes to meet

young people soon though her work and church.

On the first Saturday morning after she moved into her new

apartment, Kim decided to get up early and go jogging. It was

still dark out, but Kim was not afraid. She had been jogging

alone in the dark many times in her hometown. She donned her

jogging clothes and headed down the quiet street toward a nearby

park. As she entered the park, an individual came out from a

dense clump of bushes, put a knife to her throat, and ordered her

to the ground. She was raped and beaten unconscious. She

remained in that condition until sunrise when she was found by

another jogger who called emergency services, and Kim was

taken to the nearest emergency department. Upon regaining

consciousness, Kim was hysterical, but a sexual assault nurse

examiner (SANE) was called to the scene, and Kim was assigned

to a quiet area of the hospital, where the post-rape examination

was initiated.

Answer the following questions related to Kim:

1. What are the initial nursing interventions for Kim?

2. What treatments must the nurse ensure that Kim is aware

are available for her?

3. What nursing diagnosis would the nurse expect to focus on

with Kim in follow-up care? 

Kim is a 27-year-old woman who recently moved from a small town in Texas to work in the city of Dallas as a reporter for one of the major newspapers. She is 5’6” tall and weighs 115 lb. To keep in shape she likes to jog, which she did regularly in her hometown. She doesn’t know anyone in Dallas and has been lonely for her family since arriving. But she has moved into a small apartment in a quiet neighborhood and hopes to meet young people soon though her work and church. On the first Saturday morning after she moved into her new apartment, Kim decided to get up early and go jogging. It was still dark out, but Kim was not afraid. She had been jogging alone in the dark many times in her hometown. She donned her jogging clothes and headed down the quiet street toward a nearby park. As she entered the park, an individual came out from a dense clump of bushes, put a knife to her throat, and ordered her to the ground. She was raped and beaten unconscious. She remained in that condition until sunrise when she was found by another jogger who called emergency services, and Kim was taken to the nearest emergency department. Upon regaining consciousness, Kim was hysterical, but a sexual assault nurse examiner (SANE) was called to the scene, and Kim was assigned to a quiet area of the hospital, where the post-rape examination was initiated. Answer the following questions related to Kim: 1. What are the initial nursing interventions for Kim? 2. What treatments must the nurse ensure that Kim is aware are available for her? 3. What nursing diagnosis would the nurse expect to focus on with Kim in follow-up care?

Penny Lawrence is a research scientist in Miama, Florida. Her husband Lary Lawrence stays home to take care of their two young children, George (age 11) and Allie (age 9). Penny's total wages for 2019 were $73,023 from which $6,418 of federal income tax was withheld.  Florida does not have a state income tax.

They had $213 in interest income. Penny received dividends from Exxon in the amount of $434 and Lary received dividends from First National Bank in the amount of $324.   The additionally received interest on a State of Florida bond in the amount of $42.  They gave $4,418 to their church, $2000 to the Committee to Elect Sam Spade, and gave a bag of clothing valued at $471 to the Salvation Army (they have a receipt).   The Kenzie’s paid taxes on their house in the amount of $3,210.

Penny attended the University of Florida and is still paying off her student loans.  She paid $4800 in student loans this year, and $196 of that amount was interest.

The Lawrence’s paid $6,281 in medical insurance premiums (after tax dollars).  They also paid $523 in doctor’s visits and $481 for new glasses. Penny Lawrence is a big believer in vitamins and spent $522 at the GNC this year on supplements.

The Lawrence’s mortgage payment is $1,546 per month.  80% of their total mortgage payment is interest. Penny receives child support from her ex-husband in the amount of $300 per month. They were divorced in 2014.

Lary likes to play the nickel slots.  He went to Las Vegas for a trip with the guys.  He won $2,291 on the slot machines.  He didn’t tell Penny, however, that it cost him in nickels $1,143 to win that money.

Prepare the Penny's 2019 Form 1040 tax return and any necessary schedules.  Calculate their 2019 federal income tax and determine if they owe additional taxes or are receiving a refund.