This assignment must be created as a Quarto document in RStudio, Rendered to PDF

This assignment must be created as a Quarto document in RStudio, Rendered to PDF.
a) Begin by creating a brand new Quarto file. Set your name to your full (registered in the course) name and student number (e.g., “Jane Smith – 0612345”) and the title to “MATH 1051H – R Assignment 4”
b) Set the Default Output Format to PDF
2. The assignment must be turned in (that means created AND uploaded) digitally as a Rendered PDF – any other format will not be graded, and you will receive a ZERO grade. This will be fully enforced for this assignment. No screenshots, and definitely no screenshots of RStudio non-rendered.
3. Save your Quarto file to a file name without any spaces in it (suggestion: 1051H_r4.qmd).
Questions (each must be created as its own section, using ## in Quarto, with appropriate header descriptions). Do not number the questions in the Quarto document. See the note above about the newpage command.
1. Academic Integrity
Please copy the following statement as the first question of your submission, under the heading “Academic Integrity”.
I am aware that I can discuss the questions on this assignment with others. However, showing my files or code to another student (allowing them to copy), or having someone show their files or code with me (copying), in any way is considered cheating and will be penalized according to Trent’s Academic Integrity policies.
Questions 2, 3, 4, 5
Answer the following four word problems. Make each its own ## section, with context-correct headers (not ‘Question 2’ or similar!). You are expected to follow the full process of answering a hypothesis test and/or confidence interval, as demonstrated in Lectures 13-17. The only use of the “Question 2” versus “3” is to upload each solution separately to CrowdMark for ease of grading. Put newpage between each solution.
 An apple farmer has a contract to provide apples to a local supermarket. The contract specifies the apples, on average, must be at least 100g. The farmer delivers a pallet of boxes of apples to

the store. The store selects one box, and finds that the 107 apples in the box weigh 95.4g on average. They know that historically the standard deviation of the weight of an apple from this orchard is 10g. Create a visualization to go along with your calculation of the star value, and then compute an 89% confidence interval for the true mean weight of apples on this pallet.
 Consider a scenario where a car magazine wants to test if the average gas mileage of a new model is significantly different from the advertised value, as they are getting write-in complaints from their readership. The advertised gas mileage is 30 miles per gallon (mpg), and the car magazine collects a random sample of 25 cars. The observed gas mileage (in mpg) for each car in the sample is as follows:
28, 31, 29, 32, 30, 33, 31, 30, 29, 28, 30, 32, 29, 31, 33, 31, 30, 29, 31, 32, 30, 28, 32, 29, 31
Determine if the average mileage is significantly different to the advertised value of 30 mpg, with a formal conclusion.
 Suppose you are a researcher investigating the effects of a new educational program on students’ math performance. You have two groups: a control group that follows the traditional teaching method, and an experimental group that receives the new program. You want to determine whether the new program has a significant impact on students’ math scores, so you’re going to compare the experimental group to the known traditional results, which for this course is a mean score of 78. Your data is 28 samples:
88, 92, 90, 87, 93, 88, 86, 91, 89, 90, 92, 87, 91, 89, 88, 90, 93, 92, 89, 86, 88, 90, 91, 92, 87, 89, 88, 90
Compare this sample to the known traditional result, and determine if the experimental program is associated with an improvement in average score. BONUS: for one bonus mark, create a complete visualization for the p-value associated with this test.
 A company claims that 75% of its customers are satisfied with their product. However, you are skeptical of this claim. You randomly select 200 customers and ask them if they are satisfied with the product. Out of the 200 customers, 145 indicate that they are satisfied. Determine if there is enough evidence to support the company’s claim.