below are the questions and i will attach the note if you need ---title: "Question 1"--- ```{r, message = FALSE}library(tidyverse)library(gapminder)# use ?gapminder get the desciption of the dataset `gapminder```` Consider the dataset `gapminder`. ##### (a) Modify the `continent` factor by classifying the Americas' countries into `South America` and `North America` Hint: the following countries are in South America. ```r c("Argentina", "Bolivia", "Brazil", "Chile", "Colombia", "Ecuador", "Paraguay", "Peru", "Trinidad and Tobago", "Uruguay", "Venezuela") ``` In the following questions, use the dataset modified in (a). Hint: you could use `case_when` function. ##### (b) How many countries are there in the dataset? How about for each continent? ##### (c) For each year, which country had the largest gdp per capital? ##### (d) For each continent, which country experienced the sharpest increment rate in life expectancy from 1997 to 2007? ##### (e) Focus on the data in year 2007, what are the correlation coefficients between life expectancy and gdp per capital for each continent? ##### (f) Visualize part (e) by plotting gdp per capital vs life expectancy.---title: "Question 2"--- Consider the `flights` dataset in the package `nycflights13`. ```{r, message = FALSE}library(nycflights13)library(tidyverse)``` ##### (a) Add a column that is the amount of time gained in the air (`gain = dep_delay - arr_delay`) ##### (b) Sort part (a) descedingly by the column you just created. Store the result as `flights_gain`. ##### (c) On average, did flights gain or lose time? (Hint: not average gain, but as percentage of positive gain.) ##### (d) On average, did flights heading to SeaTac ("SEA") gain or loose time? ##### (e) Summerize the mean, min and max of the `air_time` column for flights from `JFK` to `SEA`. ##### (f) In which month was the average departure delay the greatest? ##### (g) In which airport were the average arrival delays the highest? #####(h) Which city was flown to with the highest average speed? ##### (i) Create a data frame of the average arrival delay for each destination, then use` left_join` to join on the `airports` dataframe, which has the airport info. (Hint: read the documentation of `airports` for the airport codes.)---title: "Question 3"--- ##### (a) There is a csv file called `groceries.csv` in this directory. Read the csv file using `read_csv` from `tidyverse` and store the data frame as `groceries`. The datset shows the prices of some common groceries item in 4 different stores. The table shows the prices of different items in 4 different stores. ##### (b) Is the data frame in wide format or long format? ##### (c) Try to convert it into the other format. Store it as `groceries2`. ##### (d) Use a randomized block design to analysis the store prices. Is there a store marking up the item prices?

Case Study: Statistical Inference Overview The research department of an appliance manufacturing firm has developed a solid-state switch for its blender that the research department claims will reduce appliance returns under the one-year full warranty by 3%–6%. To determine if the claim can be supported, the testing department selects a group of the blenders manufactured with the new switch and a group with the old switch and subjects them to a normal year’s worth of wear. Out of 250 blenders tested with the new switch, nine would have been returned. Sixteen would have been returned out of the 250 blenders with the old switch. As the manager of the appliance manufacturing process, use a statistical procedure to verify or refute the research department’s claim.