Census Sampling
1. The problem asks about the concepts of census and sampling in various scenarios related to schools, factories, councils, manufacturers, and garages.
2. For question 1a, a census means collecting data from every member of the population.
3. For 1b, an advantage of a census is accuracy as every member is included. A disadvantage is that it is time-consuming and expensive.
4. For 2a, a census would not be used because testing every one of 3,000 harnesses would be time-consuming and costly.
5. For 2b and 2c, the sample data of breaking loads are 310 kg, 250 kg, 240 kg, 180 kg. Since some harnesses break below 250 kg, the factory might reject the batch as not all are safe, or improve production to increase consistency above 250 kg.
6. For 3a, the city council should not take a census because it may be too large and costly.
7. For 3b, sampling units could be residents selected randomly to represent the population.
8. For 4a, the sampling frame is the list or set of all microwave switches available for testing.
9. For 4b, a suitable sampling frame might be recent production batches or serial numbers.
10. For 4c, the sample data are 2150, 2501, 1940, 2292, and 745 cycles. The average is $$\frac{2150 + 2501 + 1940 + 2292 + 745}{5} = \frac{9638}{5} = 1927.6$$ cycles. Since this average is less than 2000, it suggests the claim that the switches can last 2000 cycles on average is questionable.
11. For 5a, the population is all the mechanics working in the garage.
12. For 5b, an advantage of asking all mechanics is complete and accurate feedback with no sampling error.
Final answers summarize these points as explained above.