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Answer :
The random condition is met, and the Large Counts condition is met. The correct answer is D. Yes, all of the conditions for inference are met.
To determine if the conditions for inference are met in this scenario, we need to evaluate three key conditions: random sampling, independence, and sample size.
A. Random condition: If the sample of 150 students is selected randomly from the population of students at the university, then the random condition is met. Random sampling helps ensure that the sample is representative of the population.
B. 10% condition: The 10% condition states that the sample size should be less than 10% of the total population. Without information about the total number of students at the university, we cannot determine if the 10% condition is met. Therefore, we cannot conclude that it is not met.
C. Large Counts condition: The Large Counts condition applies to categorical data and states that the expected counts in each category should be at least 5. In this case, the expected count for the cafeteria option is 0.7 x 150 = 105, which is greater than 5. For the other three options, the expected count is 0.1 x 150 = 15, which is also greater than 5. Therefore, the Large Counts condition is met.
Based on the information given, we can conclude that the random condition is met, and the Large Counts condition is met. However, we do not have enough information to determine if the 10% condition is met. Therefore, the correct answer is D. Yes, all of the conditions for inference are met.
To learn more about the random sampling;
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