Z-test and Confidence Intervals | IB Math AIHL | Perplex

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Topics

Exponents & Logarithms Approximations & Error Sequences & Series Matrices Complex Numbers Financial Mathematics

Cartesian plane & lines Function Theory Modelling Transformations & asymptotes

2D & 3D Geometry Voronoi Diagrams Trig equations & identities Vectors Graph Theory

Probability Descriptive Statistics Bivariate Statistics Distributions & Random Variables Inference & Hypotheses

Differentiation Integration Differential Equations

Review Videos Formula Booklet My Progress

Blog Landing Page

Inference & Hypotheses (Lesson 5/6)

Z-test and Confidence Intervals

1 / 20

Discussion

A machine cuts precision parts for use in airplanes. The time, X seconds, taken to cut each part is normally distributed with a standard deviation of 12, but known mean:

X∼N(μ,122)

The quality control engineer samples the time taken to manufacture 8 parts:

45,47,49,51,53,55,57,59

(a)

What's the best guess the engineer can make for the average μ?

Solution:

The machine’s average cutting time is unknown, so the best single guess is the sample average. With the eight times 45, 47, 49, 51, 53, 55, 57, 59, notice they are evenly spaced and symmetric about the midpoint. So the average is the midpoint of the smallest and largest:

xˉ=245+59=52

Inference & Hypotheses (Lesson 5/6)

Z-test and Confidence Intervals

1 / 20

Discussion

A machine cuts precision parts for use in airplanes. The time, X seconds, taken to cut each part is normally distributed with a standard deviation of 12, but known mean:

X∼N(μ,122)

The quality control engineer samples the time taken to manufacture 8 parts:

45,47,49,51,53,55,57,59

(a)

What's the best guess the engineer can make for the average μ?

Solution:

The machine’s average cutting time is unknown, so the best single guess is the sample average. With the eight times 45, 47, 49, 51, 53, 55, 57, 59, notice they are evenly spaced and symmetric about the midpoint. So the average is the midpoint of the smallest and largest:

xˉ=245+59=52