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Lecture 18

# STAT 101 Lecture Notes - Lecture 18: Confidence Interval, Sample Size Determination, Odds RatioPremium

Department

StatisticsCourse Code

STAT 101Professor

Richard WatermanLecture

18This

**preview**shows half of the first page. to view the full**3 pages of the document.**Stat 101 - Introduction to Business Statistics - Lecture 18: Interpreting Confidence

Intervals, Finding Sample Size, & Hypothesis Testing

Interpreting a Confidence Interval

● Correct:

○ 95% of intervals created according to this procedure are expected to contain µ.

● Incorrect:

○ There is a 95% probability that µ lies in the interval.

Manipulating Confidence Intervals

● You are allowed to transform the ends of the confidence interval to obtain a new

confidence interval for the transformed parameter

○ However transformation must be monotone though -- which means if the

relationship function doesn’t just increase or decrease

● Ex) You have a 95% CI for the average miles per gallon for cars: (17.42, 18.230). Find a

95% CI for fuel economy when it is measured in liters per 100 kilometers. The transform

from MPG to ltrs./100km

○

○ The interval on the transformed scale is {F(18.23), F(17.42)} = (12.903

ltrs./100km, 13.503 ltrs./100km).

● Ex) In many medical settings clinicians like to report results in terms of odds ratios rather

than probabilities. If the probability is given by p then the odds ratio is p/(1 − p). A study

has found the 95% confidence interval for p to be (0.35, 0.38). Find the 95% CI for the

odds ratio.

○ (0.35/0.65, 0.38/0.62) = (0.538, 0.613).

Sample Size

● Must consider:

○ What confidence level you want (say 95%).

○ You need an estimate for σ.

○ What Margin of Error (MoE) you want.

■ Margin of error is the distance from the center to the edge of the interval

■Given by MoE = 1.96 /√ n σ

● Sample size:

○

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