For each situation below identify the population and the sample, and explain what p and pn represent and what the value of pn is. Would you trust a confidence interval for the true proportion based on these data? Explain briefly why or why not.

a) A manufacturing company is reporting the lifetime of the LEDs manufactured in its factory. In the report, it states that the LEDs have an average lifetime of up to 50,000 hours, which is determined from a sample of 1000 LEDs. This is approximately 50 times longer than a typical incandescent bulb, 20–25 times longer than a typical halogen, and 8–10 times longer than a typical CFL.

b) A research study was conducted to investigate the intention to retire before the statutory age in a city with about 56,785 working people. E-mails were sent out to these working people. From a sample of 2,500 participants, 1415 participants stated that it was their intention to retire before the statutory age.

c) An automobile company is estimating the percentage of adults living in a housing area who have their own automobile.

Eight hundred randomly selected adult residents in the housing area are surveyed, of whom 721 responded and 625 said they own automobiles.