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Answer :
Final answer:
The average weight of a random sample from a class may not be equal to the class mean due to sample variability. Calculating average class size involves weightings and hypothesis testing uses sample data to test claims against assumed proportions. When the population standard deviation is known, normal distribution can be used for inference.
Explanation:
The average weight of the students in a random sample from an econometrics class is not guaranteed to be exactly 145 lb, even though the class mean weight is 145 lb. This is because, in a small sample, there is variability, and the weights of just those few students may differ from the class average. The expected value of the sample mean is 145 lb, but the actual value can vary due to random sampling error.
When a statistician talks about the average class size in a university, they sum the total seats available in all classes and divide it by the number of classes. For the Summer 2013 term scenario referenced, the calculation would involve the individual class capacities weighted according to the number of such classes and divided by the total number of classes to find the expected average size.
In regards to the testing of a claim using a sample, such as the teacher's claim about students feeling more enriched after a class, a hypothesis test can be conducted. This involves comparing the sample proportion to the claimed proportion and determining whether the observed result is statistically significant or could have occurred by chance. Similarly, when working with the weights of a group of people or the weights lifted by athletes, a normal distribution may be assumed if the population standard deviation is known, and samples are used to make inferences about the population mean.
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Rewritten by : Barada
The total weight of 80 students is 80 × 145 = 11600 lb
If a sample of four students taken, their total weight divided by 4 would not necessarily give 145lb. The weight of each of the four students could be from the lightest end of the range or could be from the heaviest end of the range.
If a sample of four students taken, their total weight divided by 4 would not necessarily give 145lb. The weight of each of the four students could be from the lightest end of the range or could be from the heaviest end of the range.
