Chi-Square Goodness of Fit (Setup) Practice Test

A manufacturer claims that defects in its products fall into 4 categories with probabilities 0.50 cosmetic, 0.20 packaging, 0.20 functional, and 0.10 missing parts. An auditor inspects 150 defective products and records the observed counts shown in the table. Which hypotheses are appropriate for a chi-square goodness-of-fit test of the claim?

Observed counts table (n = 150): Cosmetic 68, Packaging 34, Functional 36, Missing parts 12.

A local election official claims that the distribution of voters arriving at a polling place by hour is 10% from 7–8am, 25% from 8–10am, 35% from 10am–1pm, and 30% from 1–5pm. A random sample of 300 voters from election day is recorded with observed counts shown in the table. Which hypotheses are appropriate for a chi-square goodness-of-fit test?

Observed counts table (n = 300): 7–8am 24, 8–10am 90, 10am–1pm 108, 1–5pm 78.