1) Spinifex pigeons are one of the few bird species that inhabit the desert of Western Australia. The pigeons rely almost entirely on seeds for food. Sixteen of these pigeons were captured in the desert, and their crop (ie stomach) contents were examined. The mean weight (in grams) of dry seed in the pigeons crops was 1.373 grams. The standard deviation of these weights was 1.034 grams. Construct and interpret a 99% confidence interval for the true mean weight of dry seeds in crops of spinifex pigeons.
2) One of the most feared predators in the ocean is the great white shark. It is known that the white shark grows to a mean length of 21 feet; however, one marine biologist believes that great white sharks off the Bermuda coast grow much longer, owing to unusual feeding habits. To test this claim, some full-grown great white sharks were captured off the Bermuda coast, measured, and then set free. However, because the capture of sharks is difficult, costly, and very dangerous, only three specimens were sampled. Their lengths were 29, 25 and 27 feet.
(a) Find the 95% confidence interval for the true mean length of the sharks off the Bermuda coast.
(b) Use your confidence interval to make a decision about the biologist’s claim.
(c) Suppose your interval had been (17, 27) feet. What would your decision be about the biologist’s claim?
3) A meteorologist wishes to estimate the mean amount of snowfall per year in Spokane, Washington. A random sample of the recorded snowfalls for 20 years from a 140 year period produces a sample mean equal to 54.03 inches, with a standard deviation of 9.59 inches.
(a) Estimate the true mean amount of snowfall using a 99% confidence interval. Don’t forget to interpret it.
(b) Why do you suppose the meteorologist took a sample of 20 years from the entire record, rather than the most recent 20 years?
(c) To properly apply t confidence interval procedures, we like the population to be normally distributed. Do you think that might be a problem for the snowfall data?