Answer :
Since random condition, 10% condition and Large counts condition are met, all of the conditions for inference are met.
Given that,
At a large company retreat, management orders subs for lunch.
They hypothesize that 50% of the attendees will choose a turkey sub, 40% will choose a ham sub, and 10% will choose a vegetarian sub.
Before placing the order, they select a random sample of 50 attendees and determine the type of sub they prefer.
The management would like to know if there is convincing evidence that the distribution of sub preference differs from 50% turkey, 40% ham, and 10% vegetarian.
Conditions for inference are met if three conditions are met.
They are randomness, normal and independence.
Since the sample is random, random condition is met.
Normal condition is met if the sample size is reasonably large which is the Large Counts Condition.
Here sample size is >30. So it is also met.
For the condition of independence, 10% condition has to be met, which is the condition that sample size should not exceed 10% of the total population.
Here population size is not given.
Since it is a large company, we assume that the population is large enough that 10% condition is also met.
Hence all conditions are met.
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