Distribution of P-hat Practice

Instructions

Complete the following questions about the sampling distribution of \(\hat{p}\). When completed, Render the qmd file and submit the html.

Questions

Question: When can we use the normal distribution to approximate the sampling distribution of \(\hat{p}\)?
Answer:

Question: What is the mean of the sampling distribution of \(\hat{p}\)?
Answer:

Question: What is the standard deviation of the sampling distribution of \(\hat{p}\)?
Answer:

Suppose the true population proportion, \(p\), of people who support a candidate for office is 52%. We would like to learn something about a sample proportion, \(\hat{p}\), with a sample size \(n=1000\) suggesting that the candidate will lose the election (\(\hat{p}<0.50\)).

Use the following R code to answer the questions below:

phat <- 
p <-
n <- 

sigma_phat <- sqrt(p*(1-p)/n)  

Error in eval(expr, envir, enclos): object 'p' not found

z <- (phat-p) / sigma_phat

Error in eval(expr, envir, enclos): object 'phat' not found

# Left Tail:
pnorm()

Error in pnorm(): argument "q" is missing, with no default

# Right tail
1-pnorm()

Error in pnorm(): argument "q" is missing, with no default

Question: What is the \(z\)-score associated with \(\hat{p}<0.5\)?
Answer:

Question: What is the standard deviation of \(\hat{p}\)?
Answer:

Question: What is the probability of a sample of size \(n=1000\) suggesting that the candidate will lose even if the true population support, \(p=0.52\)?
Answer: