Goodness-of-Fit Test · Exercise 30

Read the statement and decide whether it is true or false.

A sample of 212 commercial businesses was surveyed for recycling one commodity; a commodity here means any one type of recyclable material such as plastic or aluminum. shows the business categories in the survey, the sample size of each category, and the number of businesses in each category that recycle one commodity. Based on the study, on average half of the businesses were expected to be recycling one commodity. As a result, the last column shows the expected number of businesses in each category that recycle one commodity. At the 5% significance level, perform a hypothesis test to determine if the observed number of businesses that recycle one commodity follows the uniform distribution of the expected values.

$$\begin{array}{cccc}\text{Business Type}& \text{Number in class}& \text{Observed Number that recycle one commodity}& \text{Expected number that recycle one commodity}\\ \text{Office}& \text{35}& \text{19}& \text{17.5}\\ \text{Retail/Wholesale}& \text{48}& \text{27}& \text{24}\\ \text{Food/Restaurants}& \text{53}& \text{35}& \text{26.5}\\ \text{Manufacturing/Medical}& \text{52}& \text{21}& \text{26}\\ \text{Hotel/Mixed}& \text{24}& \text{9}& \text{12}\end{array}$$

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Introductory Statistics 2e · §11.2 Goodness-of-Fit Test · Exercise 30