# Untitled

unknown

plain_text

7 months ago

1.0 kB

2

Indexable

Never

^{}

# Define the z-values for the given probabilities z_alpha = qnorm(0.10, lower.tail = FALSE) # z-value for alpha = 0.10 z_beta = qnorm(0.95) # z-value for beta = 0.95 # Define the probabilities from the problem p1 = 1/2 p2 = 2/3 # Solve for n using the equation derived from setting the two expressions for c equal to each other n = ((z_alpha * sqrt(p1*(1-p1)) + p1) - (z_beta * sqrt(p2*(1-p2)) + p2))^2 / (p2 - p1)^2 n = (8.50)^2 # Solve for c using one of the equations for c c = z_alpha * sqrt(n*p1*(1-p1)) + n*p1 # Output the calculated values before rounding cat("Calculated sample size (n) before rounding:", n, "\n") cat("Calculated critical value (c) before rounding:", c, "\n") # Round n and c to be conservative as per the given solution n_rounded = ceiling(n) # Conservative rounding for n c_rounded = floor(c) # Conservative rounding for c # Output the rounded values cat("Sample size (n) after conservative rounding:", n_rounded, "\n") cat("Critical value (c) after conservative rounding:", c_rounded, "\n")

Leave a Comment