Lab 2I

Directions: Follow along with the slides, completing
the questions in **blue** on your
computer, and answering the questions in **red** in your
journal.

Space, Click, Right Arrow or swipe left to move to
the next slide.

- In the last lab, you were able to overlay a normal curve on
histograms of data to help you decide if the data’s distribution is
close to a normal distribution.
- We also saw that calculating the
`mean`

of random shuffles also produces differences that are normally distributed.

- We also saw that calculating the
- In this lab, we’ll learn how to use some other
`R`

functions to:- Simulate random draws from a normal distribution.
- Calculate probabilities with normal distributions.

- Start by loading the
`titanic`

data and calculate the`mean`

`age`

of people in the data but`shuffle`

their`survival`

status 500 times.`Assign`

this data the name`shfls`

.

- After creating
`shfls`

, use`mutate`

to add a new variable to the dataset. This new variable should have the name`diff`

and should be the`mean`

`age`

of those who survived minus those who died. - Finally, calculate the
`mean`

and`sd`

of the`diff`

variable.`Assign`

these values the name`diff_mean`

and`diff_sd`

.

- Before we proceed, we need to verify that our
`diff`

variable looks approximately normally distributed.**Is the distribution close to normal? Explain how you determined this. Describe the center and spread of the distribution.****Compute and write down the mean difference in the age of the***actual*survivors and the actual non-survivors.

Since the distribution of our

`diff`

variable appears normally distributed, we can use a normal model to estimate the probability of seeing differences that are more extreme than our actual data.**Draw a sketch of a normal curve. Label the mean age difference, based on your shuffles, and the actual age difference of survivors minus non-survivors from the actual data. Then shade in the areas, under normal the curve, that are***smaller*than the actual difference.Fill in the blanks to calculate the probability of an even smaller difference occurring than our actual difference using a normal model.

The probability you calculated in the previous slide is an estimate for how often we expect to see a difference smaller than the actual one we observed, by chance alone.

If you wanted to instead calculate the probability that the difference would be larger than the one observed, we could run (fill in the blanks):

- We can simulate random draws from a normal distribution with the
`rnorm`

function. - Fill in the blanks in the following two lines of
code to simulate 100 heights of randomly chosen men. Assume the
`mean`

height is 67 inches and the`standard deviation`

is 3 inches.

- Plot your simulated heights with a
`histogram`

.

- We’ve seen that we can use
`pnorm`

to calculate*probabilities*based on a specified*quantity*.- Hence, why we call it “P” norm.

- Now we’ll see how to do the opposite. That is, calculate a the
*quantity*for a specific*probability*.- Hence why we’ll call this a “Q” norm.

**How tall can a man be and still be in the shortest 25% of heights if the mean height is 67 inches with a standard deviation of 3 inches?**

Conduct one of the statistical investigations below:

- Using the
`titanic`

data:**Were women on the Titanic typically younger than men?****Use a histogram, 500 random shuffles and a normal model to answer the question in the bullet above.**

- Using the
`cdc`

data:**Using 500 random shuffles and a normal model, how much taller would the typical male have to be than the typical female in order for the difference to be in the upper 1% by chance alone?****How can we use this value to justify the claim that the average**`Male`

in our data is taller than the average`Female`

?