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Learn how to tell confidence intervals from error bars by checking the legend, distinguishing SD and SE, and avoiding false conclusions from overlap.
What is the central limit theorem? Explain the sampling distribution of means, its standard error, finite-variance conditions, and sample-size limits.
Select the null hypothesis for a test of independence: state H₀ and H₁ for two categorical variables and explain what a chi-square test can conclude.
What is the expected value for the binomial distribution below? Use n=100 households and p=0.65 to calculate and interpret E(X)=65 households.
Signed one-dimensional position changes give a net displacement of −0.2 km, while adding all three path segments gives a total distance of 4.6 km.
The lawn mower’s horizontal displacement receives work only from the force component parallel to motion, giving approximately 1.54 kJ for the applied force.
Under the textbook’s frictionless model, the falling rock retains 980 J of potential energy and has gained 980 J of kinetic energy after falling halfway.
Converting 0.250 mi to about 402 m and applying the no-time constant-acceleration equation gives a final dragster velocity of about 145 m/s.
The derivative of 1/(1+x) is −1/(x+1)². At x = 2, the point (2, 1/3) and slope −1/9 determine the tangent line.