1) Overproduction of uric acid in the body can be an indicationof cell breakdown. This may be an advance indication of illnesssuch as gout, leukemia, or lymphoma.†Over a period of months, anadult male patient has taken eight blood tests for uric acid. Themean concentration was x = 5.35 mg/dl. The distribution ofuric acid in healthy adult males can be assumed to be normal, withσ = 1.93 mg/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.)
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margin of error |
(d) Find the sample size necessary for a 95% confidence levelwith maximal margin of error E = 1.06 for the meanconcentration of uric acid in this patient's blood. (Round youranswer up to the nearest whole number.)
2) Allen's hummingbird (Selasphorus sasin) has beenstudied by zoologist Bill Alther.†Suppose a small group of 10Allen's hummingbirds has been under study in Arizona. The averageweight for these birds is x = 3.15 grams. Based onprevious studies, we can assume that the weights of Allen'shummingbirds have a normal distribution, with σ = 0.34gram.
(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.)
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(d) Find the sample size necessary for an 80% confidence levelwith a maximal margin of error E = 0.08 for the meanweights of the hummingbirds. (Round up to the nearest wholenumber.)
3) How hot is the air in the top (crown) of a hot air balloon?Information from Ballooning: The Complete Guide to Riding theWinds, by Wirth and Young (Random House), claims that the airin the crown should be an average of 100°C for a balloon to be in astate of equilibrium. However, the temperature does not need to beexactly 100°C. What is a reasonable and safe range of temperatures?This range may vary with the size and (decorative) shape of theballoon. All balloons have a temperature gauge in the crown.Suppose that 52 readings (for a balloon in equilibrium) gave a meantemperature of x = 97°C. For this balloon, σ≈18°C.
(a) Compute a 95% confidence interval for the averagetemperature at which this balloon will be in a steady-stateequilibrium. (Round your answers to one decimal place.)
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