Math Problem Statement
A learn-to-type software program claims that it can improve your typing skills. To test the claim and possibly help yourself out, you and five of your friends decide to try the program and see what happens. Use the table below to construct a 99% confidence interval for the true mean change in the typing speeds for people who have completed the typing program. Let Population 1 be the typing speed before taking the program and Population 2 be the typing speed after taking the program. Round the endpoints of the interval to one decimal place, if necessary.
Typing Speeds (in Words per Minute) Before After 34 33 30 35 50 36 53 46 33 35 47 43
Solution
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Math Problem Analysis
Mathematical Concepts
Confidence Intervals
Paired Data Analysis
Statistics
T-Distribution
Formulas
Mean difference formula: \( \bar{d} = \frac{\sum d_i}{n} \)
Standard deviation formula: \( s_d = \sqrt{\frac{\sum (d_i - \bar{d})^2}{n-1}} \)
Confidence interval formula: \( \bar{d} \pm t^* \times \frac{s_d}{\sqrt{n}} \)
Theorems
Central Limit Theorem
T-Distribution
Suitable Grade Level
Grades 11-12, Introductory College
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