Testing whether green quilts are preferred

Question

A shop sells quilts in three colours: blue, red and green. Among its first $1000$ sales, $400$ were green. Compute the test statistic for whether buyers favour green over the other colours, using a normal approximation and assuming random sampling.

Short answer

$z\approx4.47$ . Under no preference each colour has share $\tfrac13$ , so test $H_0:p=\tfrac13$ against $p>\tfrac13$ . With $\hat p=0.4$ , $z=(0.4-\tfrac13)/\sqrt{\tfrac13\cdot\tfrac23/1000}\approx4.47$ , strong evidence of a preference for green.

Adapted from OpenQuant; question and answer rewritten by SelfMadeQuant.com.

See the hint and the full worked solution in the question bank (free account).

Open the worked solution

Lessons behind this question

The Hypothesis Testing Framework
Covariance and Correlation
Pivotal Quantities and Exact Confidence Intervals

Start with a free lesson: Expectation, Variance and Covariance is part of a free topic. Create a free account, no card needed, to read it in full with worked solutions.

Read it free