Part #1

Allen's hummingbird (Selasphorus sasin) has been studied byzoologist Bill Alther.† Suppose a small group of 13 Allen'shummingbirds has been under study in Arizona. The average weightfor these birds is x = 3.15 grams. Based on previous studies, wecan assume that the weights of Allen's hummingbirds have a normaldistribution, with σ = 0.32 gram.

(a) Find an 80% confidence interval for the average weights ofAllen's hummingbirds in the study region. What is the margin oferror? (Round your answers to two decimal places.)

lower limit

upper limit

margin of error

(d) Find the sample size necessary for an 80% confidence levelwith a maximal margin of error E = 0.07 for the mean weights of thehummingbirds. (Round up to the nearest whole number.)

Part #2

Overproduction of uric acid in the body can be an indication ofcell breakdown. This may be an advance indication of illness suchas gout, leukemia, or lymphoma.† Over a period of months, an adultmale patient has taken thirteen blood tests for uric acid. The meanconcentration was x = 5.35 mg/dl. The distribution of uric acid inhealthy adult males can be assumed to be normal, with σ = 1.91mg/dl.

(a) Find a 95% confidence interval for the population meanconcentration of uric acid in this patient's blood. What is themargin of error? (Round your answers to two decimal places.)

lower limit

upper limit

margin of error

(d) Find the sample size necessary for a 95% confidence levelwith maximal margin of error E = 1.06 for the mean concentration ofuric acid in this patient's blood. (Round your answer up to thenearest whole number.)