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STAT 20: Introduction to Probability and Statistics

- Concept Questions
- Lab 5

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?

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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?

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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?

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What will happen to the shape of the **empirical distribution** as we increase \(n\)?

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What will happen to the shape of the **sampling distribution** as we increase \(n\)?

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```
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?

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