The table below gives the number of hours spent unsupervised each day as well as the overall grade averages for seven randomly selected middle school students. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting the overall grade average for a middle school student based on the number of hours spent unsupervised each day. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.

Step 1 of 6: Find the estimated slope. Round your answer to three decimal places.

Step 2 of 6: Find the estimated y-intercept. Round your answer to three decimal places.

Step 3 of 6: Determine if the statement "Not all points predicted by the linear model fall on the same line" is true or false.

Step 4 of 6: Find the estimated value of y when x=53x=53. Round your answer to three decimal places.

Step 5 of 6: Substitute the values you found in steps 1 and 2 into the equation for the regression line to find the estimated linear model. According to this model, if the value of the independent variable is increased by one unit, then find the change in the dependent variable yˆy^.

Step 6 of 6: Find the value of the coefficient of determination. Round your answer to three decimal places.

1. Indicate what type of statistical analysis you use to answer the following research question. We are interested in determining if there is a difference in total income based on political affiliation (republican, democrat, independent, other).

• A. Correlation

• B. One-Sample t-Test

• C. One-Way ANOVA

• D. Paired t-Test

• E. Independent t-Test

2. Indicate what type of statistical analysis you use to answer the following research question. Is the amount of time someone spends on Twitter associated with their IQ scores?

• A. Independent t-Test

• B. Paired t-Test

• C. Correlation

• D. One-Way ANOVA

• E. One-Sample t-Test

3. Indicate what type of statistical analysis you use to answer the following research question. Is the level of Social Media Addiction (continuous scale) differ based on their level of education (no high school, high school graduate, some college, BA/BS, graduate degree)?

• A. One-Way ANOVA

• B. One-Sample t-Test

• C. Correlation

• D. Paired t-Test

• E. Independent t-Test

4.Indicate what type of statistical analysis you use to answer the following research question. Is an individual’s stress level associated with the amount of time they spend in quarantine?

• A. Independent t-Test

• B. One-Way ANOVA

• C. Paired t-Test

• D. One-Sample t-Test

• E. Correlation

Imagine that you have decided to open a small ice cream stand on campus called "Ice-Campusades." You are very excited because you love ice cream (delicious!) and this is a fun way for you to apply your business and economics skills! Here is the first month's scenario--you order the same number (and the same variety) of ice creams each day from the ice cream suppliers, and your ice creams are always marked at $1.50 each. However, you notice that there are days when ice creams remain unsold but other days when there are not enough ice creams for the number of customers.

Use your knowledge of the factors that cause shifts in demand, and in a multi-paragraph essay, provide at least three reasons why ice cream sales fluctuate in this manner. (Apply only the factors you think are applicable to explaining this scenario.) Now assume that a month later, the school allows a competing student the right to sell ice creams on school property. (The number of students on campus remains largely unchanged.) What do you think will happen to the price of ice cream at your campus? Explain in detail.

Develop a response that includes examples and evidence to support your ideas, and which clearly communicates the required message to your audience. Organize your response in a clear and logical manner as appropriate for the genre of writing. Use well-structured sentences, audience-appropriate language, and correct conventions of standard American English.

Previous research suggests that musicians process music in the same cortical regions in

which adolescents process algebra. So, a researcher wondered if receiving music

instruction while learning algebra would improve students’ grasp of algebra. On the other

hand, the researcher also thought it was possible that the addition to students’ already

crowded work and course schedules might give them less time to study and complete

algebra homework. So, to examine the connections between musical instruction and

algebra skills, the researcher collected data on a sample of 6,026 ninth grade students in

Maryland who had completed introductory algebra. Of these students, 3,239 received

formal music instruction (either choral or instrumental) during all three years of middle

school, while the remaining students had not. Of those receiving formal music instruction,

2,818 received a passing grade on the Maryland Algebra/Data Analysis High School

Assessment (HAS). In contrast, 2,091 of the 2,787 students who did not receive musical

instruction received a passing grade on the HAS. Is there a difference in the proportion

passing the HAS between students with and without formal musical instruction? To answer

this question, complete a two‐sample Z test with the following steps

1. State hypotheses in sentences and notation.
2. Calculate the pooled sample proportion.
3. Compute the Z test statistic.
4. Estimate the p‐value that corresponds to the test statistic.
5. State your conclusion in reference to the null hypothesis. (Use α = .01)
6. Interpret your result in reference to the alternative hypothesis.

You are conducting a study to determine if there is a relationship between annual household income and a high school student’s GPA. The school district you are studying is diverse and lower income. a) Before you conduct the study, do you expect there to be an association between these two variables? Why or why not? Which should be the explanatory variable? b) You collect data from a random sample of 15 students. The first row of the table is household income of a particular student (in thousands of dollars) and the second row is the GPA of that particular student. 42 30 82 19 29 44 90 55 17 62 51 30 9 39 42 3.1 2.6 3.8 2.7 2.3 3.5 3.8 3.2 2.4 3.3 3.1 2.8 1.6 3.4 3.2 c) Does the data have a scatterplot that shows a linear association? What is the correlation coefficient? What does it tell you about the association between these two variables? d) Use the above data to make a linear (regression) model. e) Use the model to predict the GPA of a high-schooler that comes from a family that has a household income of $48,000. f) How accurate is the model’s prediction of GPA for the family that makes $44,000? g) If a family’s income increases by $10,000, what is the amount of change in a student’s GPA, as predicted by the model? h) Statisticians often state “correlation is not necessarily causation.” Would it be correct to conclude that household income is “causing” GPA? Is it possible that there are other variables that are “lurking,” causing GPA and household income to be correlated? What might these variables be?

Directions:

Below you will find a series of proposed solutions to problems. For each one, you are tasked with developing 3 justifications for that solution - one through consequence, one through principle, and one through either precedent or analogy. Because you will need three answers for each, you will end up with 15 answers total.

EXAMPLE:

Solution: Spanking Children should be made illegal

Justification through Principle: because it is wrong to cause bodily pain to children

Justification through Consequence: because it teaches children that it is ok to hit someone out of anger

Justification through Analogy: because spanking a child is like banging your fists against a wall - it relieves your anger but turns the child into an object

JUSTIFY THE FOLLOWING SOLUTIONS:

1. Problem: How to improve school? Solution: The school year should be extended to eleven months.

2. Problem: How to reduce obesity in our city? Solution: Our city should require all restaurants to post the calorie content of every menu item.

3. Problem: How do we reduce mass shootings? Solution: Federal law should ban large ammunition clips for automatic weapons.

4. Problem: How do we reduce overcrowding in federal prisons? Solution: The federal government should legalize marijuana.

5. Problem: How do we reduce our carbon footprint? Solution: The federal government should enact a substantially increased tax on gasoline.

The table below gives the number of hours spent unsupervised each day as well as the overall grade averages for seven randomly selected middle school students. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting the overall grade average for a middle school student based on the number of hours spent unsupervised each day. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.

Step 1 of 6: Find the estimated slope. Round your answer to three decimal places.

Step 2 of 6: Find the estimated y-intercept. Round your answer to three decimal places.

Step 3 of 6: Find the estimated value of y when x=0.5. Round your answer to three decimal places.

Step 4 of 6: Determine if the statement "All points predicted by the linear model fall on the same line" is true or false.

Step 5 of 6: Substitute the values you found in steps 1 and 2 into the equation for the regression line to find the estimated linear model. According to this model, if the value of the independent variable is increased by one unit, then find the change in the dependent variable yˆ.

Step 6 of 6: Find the value of the coefficient of determination. Round your answer to three decimal places.

In order to determine if the lexical development of kids is associated with their physical development, data had been collected among the kids of preliminary school. In a simple random sample of size n = 5, the level of lexical development has been determined as the number of words of an individual`s active vocabulary. The level of physical development had been measured as the body size or length (in cm) of an individual, i.e. the distance between the soles of the feet and the crest of the person in an upright and straight posture (see table 1).

The mean size of the kids in this sample is 127cm. The standard deviation of the size of the kids in this sample is 16 cm.

The mean number of words in the active vocabulary of the kids in this sample is 503.2.

The standard deviation of the number of words in the active vocabulary of the kids in this sample is 160.01

a. In order to describe the relationship between the lexical and physical development of the children in the given school, compute the linear correlation coefficient based on the sample data given in table 1.

b. Describe the properties of the linear correlation coefficient in general and interpret the results of subtask a accordingly!

c. Describe which possible explanation have to be considered when interpreting scatter diagrams and correlation coefficients that indicate a strong linear correlation between two variables. Interpret the results of subtask a accordingly!

d. Do a simple linear regression and determine the equation that describes best the relationship between the variables of the given set of bivariate data.

e. Determine and interpret the coefficient of determination for the model that you determined in d.

Change in Estimate versus Error Correction Facts: Your company, PlumbAll, provides routine and quick response plumbing services to a range of corporate customers. Customers are expected to pay on the first of each month, in advance of receiving services. One of your customers is a private school that has been a longtime customer. The customer has not paid for the last four months of services (September–December 20X1); nevertheless, to maintain a positive relationship, your company continued to provide services during that time. Your company ceased providing services in January 20X2 and found out in that same month that the school filed for bankruptcy in August. You now believe that the collection of the missed payments is extremely unlikely. Your company has already issued financial statements to lenders (for the period ending 12/31/X1) that reflected revenue and a corresponding account receivable related to this customer of $11,000 per month for services provided to this customer. Those financial statements also reflected the company’s standard allowance (reserve) amount on receivables of 3% of sales. In total, your company’s average monthly sales amount to $300,000.

Required:

1. Evaluate whether receipt of this information indicates you have a change in estimate or whether the customer’s bankruptcy results in this event being considered an error in previously issued financial statements.

2. Describe the accounting treatment required by the Codification for each alternative. Support your explanations with draft journal entries.

3. Briefly state which treatment appears to be more appropriate given the circumstances, describing any assumptions you made in concluding.

For the data in the Excel file Education and Income, find 95% confidence intervals for the mean annual income of males and the mean annual income of females. Can you conclude that the mean income of one group is larger than the other?