Chi-Square Goodness of Fit (Test) Practice Test

A wildlife biologist expects, based on a long-term model, that sightings of a bird species across 5 habitats occur in proportions: 0.15 Wetland, 0.25 Forest, 0.20 Grassland, 0.30 Shrubland, 0.10 Urban. In a random sample of 500 sightings, the observed counts are: Wetland 92, Forest 118, Grassland 93, Shrubland 146, Urban 51. A chi-square goodness-of-fit test gives $p$-value = 0.049.

Expected counts under $H_0$ are: Wetland 75, Forest 125, Grassland 100, Shrubland 150, Urban 50.

What conclusion is appropriate at $\alpha=0.05$?

A university expects the distribution of students’ primary commute methods to be: 50% Car, 20% Bus, 15% Bike, 10% Walk, 5% Other. A random sample of 300 students reports: Car 141, Bus 72, Bike 39, Walk 33, Other 15. A chi-square goodness-of-fit test of $H_0$: the population distribution matches the expected proportions yields $p$-value = 0.27.

Expected counts under $H_0$ are: Car 150, Bus 60, Bike 45, Walk 30, Other 15.

What conclusion is appropriate at $\alpha=0.05$?