• A confidence interval is a range of values that is likely to contain a population parameter with a certain level of confidence.
• A confidence interval is made up of a lower bound and an upper bound.

• The formula for a confidence interval for the mean (\(\mu\)) is:

\[ \bar{x} \pm t \left( \frac{s}{\sqrt{n}} \right) \]

• Where:
• \(\bar{x}\) = Sample mean
• \(t\) = Critical value from the t-distribution based on the chosen confidence level
• \(s\) = Sample standard deviation
• \(n\) = Sample size

• Data Set: ‘chickwts’
• Description: An experiment was conducted to measure and compare the effectiveness of various feed supplements on the growth rate of chickens.

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• By using the following confidence interval formula: \[ \bar{x} \pm t \left( \frac{s}{\sqrt{n}} \right) \]
• We can observe the range of average growth rate among chickens in relation to different feed supplements, as presented in the table below:

  	Mean	CI_Lower	CI_Upper
  casein	323.5833	282.6440	364.5226
  horsebean	160.2000	132.5687	187.8313
  linseed	218.7500	185.5610	251.9390
  meatmeal	276.9091	233.3083	320.5099
  soybean	246.4286	215.1754	277.6818
  sunflower	328.9167	297.8875	359.9458

summary_stats = tapply(chickwts$weight, chickwts$feed, function(x) {
  mean_val = mean(x)
  ci = t.test(x)$conf.int
  c(Mean=mean_val, CI_Lower=ci[1], CI_Upper=ci[2])
})
summary_df = as.data.frame(do.call(rbind, summary_stats))
kable(summary_df) %>%
  kable_styling(font_size = 12) %>%
  scroll_box(width = "100%", height = "400px")

• I hope you enjoyed this presentation on confidence intervals! :)