Question

At wind speeds above 1000 centimeters per second (cm/sec), significant sand-moving events begin to occur. Wind speeds below 1000 cm/sec deposit sand and wind speeds above 1000 cm/sec move sand to new locations. The cyclic nature of wind and moving sand determines the shape and location of large dunes. At a test site, the prevailing direction of the wind did not change noticeably. However, the velocity did change. Sixty-three wind speed readings gave an average velocity of x = 1075 cm/sec. Based on long-term experience, σ can be assumed to be 255 cm/sec.

(a) Find a 95% confidence interval for the population mean wind speed at this site. (Round your answers to the nearest whole number.)

lower limit	cm/sec
upper limit	cm/sec

(b) Does the confidence interval indicate that the population mean wind speed is such that the sand is always moving at this site? Explain.

No. This interval indicates that the population mean wind speed is such that the sand may not always be moving at this site? Yes. This interval indicates that the population mean wind speed is such that the sand may not always be moving at this site.    Yes. This interval indicates that the population mean wind speed is such that the sand is always moving at this site.No. This interval indicates that the population mean wind speed is such that the sand is always moving at this site.

problem #2

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 50 readings (for a balloon in equilibrium) gave a mean temperature of x = 97°C. For this balloon, σ ≈ 19°C.

(a) 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.)

lower limit	°C
upper limit	°C

(b) 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.

It will go down because hot air will make the balloon rise.It will go down because hot air will make the balloon fall.    It will go up because hot air will make the balloon rise.It will go up because hot air will make the balloon fall.

problem #3

Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 19 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with σ = 0.34 gram.

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

lower limit
upper limit
margin of error

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

n is largenormal distribution of weightsσ is knownσ is unknownuniform distribution of weights

(c) Interpret your results in the context of this problem.

There is an 80% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80.    There is a 20% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.The probability to the true average weight of Allen's hummingbirds is equal to the sample mean.The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20.

(d) Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.12 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)
hummingbirds

Answer 1

Yes, This interval indicates that the population means wind speed is such that the sand is always moving at this site.

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It will go up because hot air will make the balloon rise

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There is an 80% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.