## Analysis of Variations

Complete all of the questions in bold on the PDFs on a separate document. Answer them in detail with at least 3 complete sentences for each when possible. Also, complete the full excel sheet and all of its parts according to the instructions on the attached PDFs. I will also include the two examples referenced on the pdf (10.2 and 10.11 but it says I have reached the max files: these are just references). Some data need to be graphed where mentioned in the instructions (instructions below for requirements)
GraphsIndependent = X (18 pt. , black)
Dependent = Y (18 pt. , black)
Legend (16 pt. , black)
Numerical values for X and Y (14 pt., black)
Bar graph should be in black with black border and white with black border (do under Format Data Series)Gap width = 50%

## mod 3 week 3 case normal distrobutions

Problems need to include all required steps and answer(s) for full credit. All answers need to be reduced to lowest terms where possible. If the answer is in %, show two decimal places.
The average score of a statistics class was 71 with a standard deviation of 8.What is the z score of a student with a grade of 68? (2.5 pts)
What is the z score of a student with a grade of 80? (2.5 pts)

Using the same data in #1 answer the following:Approximately 68% (one standard deviation) of the scores are between ________ and _________ (2.5 pts)
Approximately 95% (two standard deviation) of the scores are between _________ and _________ (2.5 pts)

Most values of the standard normal distribution are between __________. (3 pts)-3 and 3
0 and 1
0 and 3
1 and 3

(a) If the standard deviation of a data set is 1.3, what is the variance? (2.5 pts)(b) If the variance is 36, what is the standard deviation? (2.5 pts)
Let X have a normal distribution with mean µ= 20 and standard deviation σ = 4. Determine the area in the normal curve for which:P (X > 28) (2.5 pts)
P (X > 12) (2.5 pts)
P (X > 24) (2.5 pts)

The IQ scores of students listed below are from a SAMPLE of MATH 300 class.
IQ Scores921101059612010090981109510299931191061039110197105What is the mean IQ score? Round to the nearest whole number. (2.5 pts)
Compute the IQ scores within plus/minus one standard deviation? Two answers. Round to the nearest whole numbers. (2.5 pts)
Compute the IQ scores within plus/minus two standard deviation? Two answers. (2.5 pts)

Let X have a normal distribution with µ= 10 and standard deviation σ= 2. Transform X to the standard normal form Z and match the following probability statements:a) P(X>14) 1) P(Z<-1)b) P(X<8) 2) P(-2 < Z < 2)c) P(6 < X 2)a) is matched to ___________ (2.5 pts)b) is matched to ___________ (2.5 pts)c) is matched to ___________ (2.5 pts)
Let X have a normal distribution with mean µ= 30 and standard deviation σ= 10. Calculate P(X>40). Round to two decimal places. (4 pts)
For a standard normal variable Z, compute P(Z<1.5). Round your answer to two decimal places. (3 pts)
A larger standard deviation of a normal distribution indicates that the distribution becomes (2.5 pts)
narrower and more peaked
flatted and wider
more skewed to the right
more skewed to the left

## Introduction to Empirical Economics

only the part B
it should be completed with R. Write down your answers and codes in a R Markdown file (.rmd) using the RStudio, then generate a PDF file. Upload the R Markdown file and the PDF le to Canvas.

## cell phones lan

Once again, here is the research question for this lab.
Based on a recent study, roughly 80% of college students in the U.S. own a smartphone. Is the proportion of smartphone owners lower at this university?
Respond to each of the following in your initial post.
State your hypotheses in symbolic form and in words. (The following should be clear in your answer: the population of interest and the meaning of the proportion p in terms of the variable Cell.)
StatCrunch uses a normal model to estimate the P-value probability. Verify that normality conditions are met.
Use StatCrunch to conduct the hypothesis test. (directions)Copy and paste the results (the StatCrunch output window) into the textbox.
Give your P-value and interpret its meaning as a conditional probability.
State a conclusion that answers the research question. Use a significance level of 5%. (Be sure to state your conclusion in context. This means you should include the P-value, and reference the population and the variable Cell in your conclusion.)
We cannot know whether a Type 1 or Type 2 error actually occurs in a hypothesis test. But, based on the results of our hypothesis test, we should be aware of which type of error is possible and what that error means in the context of our test.
For the hypothesis test you conducted above, which type of error is possible, Type 1 or Type 2? Briefly explain why.
In the context of your hypothesis test, describe a potential consequence of this type of error.

## cell phones lan

Once again, here is the research question for this lab.
Based on a recent study, roughly 80% of college students in the U.S. own a smartphone. Is the proportion of smartphone owners lower at this university?
Respond to each of the following in your initial post.
State your hypotheses in symbolic form and in words. (The following should be clear in your answer: the population of interest and the meaning of the proportion p in terms of the variable Cell.)
StatCrunch uses a normal model to estimate the P-value probability. Verify that normality conditions are met.
Use StatCrunch to conduct the hypothesis test. (directions)Copy and paste the results (the StatCrunch output window) into the textbox.
Give your P-value and interpret its meaning as a conditional probability.
State a conclusion that answers the research question. Use a significance level of 5%. (Be sure to state your conclusion in context. This means you should include the P-value, and reference the population and the variable Cell in your conclusion.)
We cannot know whether a Type 1 or Type 2 error actually occurs in a hypothesis test. But, based on the results of our hypothesis test, we should be aware of which type of error is possible and what that error means in the context of our test.
For the hypothesis test you conducted above, which type of error is possible, Type 1 or Type 2? Briefly explain why.
In the context of your hypothesis test, describe a potential consequence of this type of error.

## Week 2 case 2

Problems need to include all required steps and answer(s) for full credit. All answers need to be reduced to lowest terms where possible. If the answer is in %, show two decimal places.
Below are excel functions, which you can use to solve for measures of central tendency and variability. You can use the formulas too; but, they will be time consuming.
EXCEL FUNCTIONS
Measures of Central Tendency
Suppose data are in cells A1 to A10
Mean =AVERAGE(A1:A10)
Median =MEDIAN(A1:A10)
Mode =MODE(A1:A10)
Measures of Variability
Suppose data are in cells A1 to A10
Range =MAX(A1:A10)-MIN(A1:A10)
IQR =QUARTILE.EXC(A1:A10,3)-QUARTILE.EXC(A1:A10,1)
Population Variance σ2 =VAR.P(A1:A10)
Sample Variance s2 =VAR(A1:A10) or VAR.S(A1:A10)
Population Standard Deviation σ =STDEV.P(A1:A10)
Sample Standard Deviation s =STDEV(A1:A10) or STDEV.S(A1:A10)
Joe and Mary would like to buy their first home in a new city. Below is the list of prices of 20 homes for sale.
Prices in US Dollars140190265115270240250180160200240280175200310195320105385265
Find the mean, median, mode. (2 pts)
Which measure of central tendency best represent the data? Why? (2 pts)
Are there any outliers? If so, name the outlier. (2 pts)

The ages of students in a statistics class are listed below.
Age of students2220252327301831194545193627192633403524
Create a stem plot (2 pts)
What is the mean age of the student? (2 pts)

Jenny likes to have at least a 70% average to pass her statistics class. Her previous four test scores are 52%, 66%, 76% and 71%. What is the minimum score Heidi needs on the final exam to pass the class? (4 pts)
Consider the following data and corresponding weights.
Xi Weight (wi )3.152.332.8244
Compute the weighted mean. (2 pts)
Compute the mean without weighting. (2 pts)

The chart below represents the amount of rainfall for 15 days in northern Ohio in July.
Rainfall in inches 4.14.23.53.94.24.43.83.73.53.44.33.24.34.5 4
Complete the frequency table. (2 pts)
Rainfall in inchesFrequencyLess than 3.03.0-3.43.5-3.94.0-4.5
Find the mean of the raw data. (2 pts)
Find the median of the raw data. (2 pts)
Find the mode of the raw data. (2 pts)

Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28 and 25.What is the minimum? (2 pts)
What is the first quartile? (2 pts)
What is the median? (2 pts)
What is the third quartile? (2 pts)
What is the maximum? (2 pts)

Create the box plot for the data in #6. Label the five points on the box. (4 pts)
Using the data in #6.What is the range? (2 pts)
What is the interquartile range (IQR)? (2 pts)

The histogram of a quantitative variable is positively skewed. The mean of the variable is 35.Which one of the following is a more likely value of the median? (2 pts)553035

A histogram of a given data shows three clear peaks. This may mean that (4 pts)
There are three distinct groups in the data
There are three modes in the data
Both a and b are correct

## Cell Phone Lab

Questions ranged from “How many credits are you registered for this semester?” to “Would you define yourself as a vegetarian?”
The researcher randomly selected 325 students from the university; 312 responded to the survey.
PromptOnce again, here is the research question for this lab.
Based on a recent study, roughly 80% of college students in the U.S. own a smartphone. Is the proportion of smartphone owners lower at this university?
Respond to each of the following in your initial post.
State your hypotheses in symbolic form and in words. (The following should be clear in your answer: the population of interest and the meaning of the proportion p in terms of the variable Cell.)
StatCrunch uses a normal model to estimate the P-value probability. Verify that normality conditions are met.
Use StatCrunch to conduct the hypothesis test. (directions)Copy and paste the results (the StatCrunch output window) into the textbox.
Give your P-value and interpret its meaning as a conditional probability.
State a conclusion that answers the research question. Use a significance level of 5%. (Be sure to state your conclusion in context. This means you should include the P-value, and reference the population and the variable Cell in your conclusion.)
We cannot know whether a Type 1 or Type 2 error actually occurs in a hypothesis test. But, based on the results of our hypothesis test, we should be aware of which type of error is possible and what that error means in the context of our test.
For the hypothesis test you conducted above, which type of error is possible, Type 1 or Type 2? Briefly explain why.
In the context of your hypothesis test, describe a potential consequence of this type of error.
https://www.statcrunch.com/app/index.php?dataid=37…

## Estimating a population porportion

) by Jeffrey M. Jones.
According to the article, 61% of U.S. adults who responded to the survey favor requiring College students to be vaccinated in order to attend classes (including classes in fall 2021). A representative random sample of 3,572 adults U.S. adults, aged 18 and older, were surveyed.
Are conditions met for calculating a confidence interval? Support your conclusion mathematically and show your work.
If conditions are met, use your graphing calculator to calculate a 95% confidence interval that estimates the proportion of U.S. adults who favor requiring College students to be vaccinated in order to attend classes. State your results in context.
Question 2
Open your IAT sample data set in StatCrunch (directions)
We will use a 90% confidence interval to estimate the population proportion of participants born-female in our chosen IAT data set.
So, you are tasked with using your IAT sample to calculate a 90% confidence interval that estimates the population proportion of participants born-female in your particular IAT. But, you are missing a piece of information that would allow you to use your graphing calculator to find the confidence interval. What piece of information is missing?
Even though we cannot readily use our graphing calculators, StatCrunch can calculate the confidence interval for us! Use StatCrunch to find the 90% confidence interval for the population proportion of female participants in your particular IAT (directions – opens in a new tab). Highlight and copy everything in your StatCrunch output window and paste it in your response.
Identify the sample proportion (𝑝̂ )(p^) in the StatCrunch output table. Then determine whether conditions are met for using the confidence interval to estimate the population proportion of female participants in your chosen IAT. Show your work.
If conditions are met, estimate the population proportion of female participants in your particular IAT, and state your conclusion in context. If conditions are not met, explain what a researcher could do so that conditions are met.
Based on your analysis, do you think the population of participants in your chosen IAT are representative of the U.S. population? Explain.
This is my sample data IAT https://www.statcrunch.com/app/index.php?dataid=38…

## Percentages and proportional reasoning to draw conclusions about housing affordability

Collect data:
Look up the minimum wage for Seattle, and calculate a person’s monthly earnings assuming a 40 hour work week on minimum wage.
Look up the median annual salary for Seattle.
Look up rental prices for at least 5 specific two-bedroom apartments in this city. Find a range of higher- and lower-priced selections.
2. Analyze: There is a rule of thumb that says that people should pay a maximum of 30% of their gross (pre-tax) wages for housing costs. Use the data you collected to analyze whether a person working full-time minimum wage and a person earning the median salary can afford to live in the city you chose. Here are some suggestions for values to calculate:
The percentage each person must pay of their earnings for the least, middle, and most expensive apartments on your list. Is it below 30%?
The minimum salary a person must make to afford some of the places on your list
3. Report: Create a report that presents your conclusions. Your report must include:
A table or chart that shows all the data you collected, organized however you choose
At least two paragraphs of writing that describe your conclusions. Your writing should include:
In your opinion, is the city you analyzed “affordable” to live in?
At least 4 data calculations that support your conclusion (these can be embedded into your writing or else on a separate calculations page)
Does any of this data surprise you? Or is it something you already knew?
A list of sources you used for this report.