Confidence Intervals

STAT 20: Introduction to Probability and Statistics

Agenda

• Concept Questions
• Lab 5

Concept Questions

You embark on a mission to estimate a population mean using a simple random sample of $n$ observations.

What sample size would you need to increase the precision of your estimate by approximately 3x compared to the original sample?

01:00

An economist aims to estimate the average weekly cost of groceries per household in two cites: Oakland, CA (population ~400,000) and Fremont, CA (population ~200,000). Both of these populations of households are presumed to have a similar standard deviation of weekly grocery costs. The economist takes a simple random sample (without replacement) of 100 households from each city, records their costs, and computes a 95% confidence interval for the average weekly cost.

Approximately how much wider would Oakland’s confidence interval be than Fremont’s?

01:00

An economist aims to estimate the average weekly cost of groceries per household in two cites: Grimes, CA (population ~400) and Tranquility, CA (population ~800). Both of these populations of households are presumed to have a similar standard deviation of weekly grocery costs. The demographer takes a simple random sample (without replacement) of 100 households from each city, records their costs, and computes a 95% confidence interval for the average weekly cost.

Approximately how much wider would Tranquility’s confidence interval be than Grimes’s?

02:00

What will happen to the shape of the empirical distribution as we increase $n$?

01:00

What will happen to the shape of the sampling distribution as we increase $n$?

01:00
library(stat20data)

set.seed(5)
flights %>%
slice_sample(n = 30) %>%
summarize(xbar = mean(air_time),
sx = sd(air_time),
n = n())
# A tibble: 1 × 3
xbar    sx     n
<dbl> <dbl> <int>
1  118.  81.5    30

What is an approximate 95% confidence interval for the mean air time in flights using the normal curve?

01:00