Example 1-Tailed & 2-Tailed CIs for Sample Mean 𝑋̅

2-Tailed Confidence Interval

2-Sided CI

  • 𝑧-distribution -Β [ 𝑋̅ - 𝑧𝛼/2𝑆𝐸(𝑋̅), 𝑋̅ + 𝑧𝛼/2𝑆𝐸(𝑋̅) ]
  • 𝑑-distribution -Β [ 𝑋̅ - 𝑑𝛼/2𝑆𝐸(𝑋̅),  𝑋̅ + 𝑑𝛼/2𝑆𝐸(𝑋̅) ]

1-Sided Lower CI

  • 𝑧-distribution -Β [ -∞, 𝑋̅ + 𝑧𝛼𝑆𝐸(𝑋̅)Β ]
  • 𝑑-distribution -Β [Β -∞,  𝑋̅ + 𝑑𝛼𝑆𝐸(𝑋̅)Β ]

1-Sided Upper CI

  • 𝑧-distribution -Β [ 𝑋̅ - 𝑧𝛼𝑆𝐸(𝑋̅), ∞ ]
  • 𝑑-distribution -Β [ 𝑋̅ - 𝑑𝛼𝑆𝐸(𝑋̅), ∞ ]
1-Tailed Lower Confidence Interval

1-Tailed Upper Confidence Interval