(d) How much do wild mountain lions weigh? Adult wild mountain lions (18 months

Question

(d) How much do wild mountain lions weigh? Adult wild mountain lions (18 months or older) captured and released for the first time in the San Andres Mountains gave the following weights (pounds):

Assume that the population of x values has an approximately normal distribution.

-Find a 75% confidence interval for the population average weight of all adult mountain lions in the specified region. (Round your answers to one decimal place.)

(e) How hot is the air in the top (crown) of a hot air balloon? Information from Ballooning: The Complete Guide to Riding the Winds, by Wirth and Young (Random House), claims that the air in the crown should be an average of 100°C for a balloon to be in a state of equilibrium. However, the temperature does not need to be exactly 100°C. What is a reasonable and safe range of temperatures? This range may vary with the size and (decorative) shape of the balloon. All balloons have a temperature gauge in the crown. Suppose that 55 readings (for a balloon in equilibrium) gave a mean temperature of x = 97°C. For this balloon, 23°C.

-Compute a 95% confidence interval for the average temperature at which this balloon will be in a steady-state equilibrium. (Round your answers to one decimal place.)

(f) If the average temperature in the crown of the balloon goes above the high end of your confidence interval, do you expect that the balloon will go up or down? Explain.

(a) It will go down because hot air will make the balloon fall.

(b) It will go up because hot air will make the balloon fall.     

(c) It will go up because hot air will make the balloon rise.

(d) It will go down because hot air will make the balloon rise.

Answer:_______________

(g) Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 15 Allen's hummingbirds has been under study in Arizona. The average weight for these birds isx = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with = 0.32 gram.

(a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. (Round your answers to two decimal places.)

(b) What conditions are necessary for your calculations? (Select all that apply.)

(a) is known

(b)uniform distribution of weights

(c) n is large

(d) normal distribution of weights

(e) is unknown

Answer:________?________

(c) Give a brief interpretation of your results in the context of this problem.

(d) Find the sample size necessary for an 80% confidence level with a maximal error of estimate E = 0.15 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)
____________?___________hummingbirds

67 110 134 127 60 64

Explanation / Answer

d)

at 5 degree of freedom and 75% confidence level ; t=1.3009

hence lower limit =sample mean -t*std error =75.6882

upper limit = sample mean +t*std error =111.6451

e)

here std error=std deviation/(n)1/2 =3.1013

for 95% CI, z=1.96

hence lower limit =sample mean -z*std error =90.9

upper limit =sample mean +z*std error=103.1

(c) It will go up because hot air will make the balloon rise.

g)

here std error=std deviation/(n)1/2 =0.0826

for 80% CI, z=1.2816

hence lower limit =sample mean -z*std error =3.04

upper limit =sample mean +z*std error=3.26

margin of error =z*std error =0.11

b)

a) is known

(d) normal distribution of weights

c)

for margin of error E=0.15

std deviation =0.32

for 80% CI, z=1.2816

hence samp[le size n=(z*std deviation/E)2 =~8 hummingbirds

X 67 110 134 127 60 64 mean(X) 93.667 std deviation(S) 33.851 std error =S/(n)1/2 13.819

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