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Chapter 8: Q 8.9 (page 320)

A simple randoes sample is taken from a population and yields the following data for a variable of the population:

find a point estimate for the population standard deviation (i.e., the standard deviation of the variable).

Short Answer

Expert verified

The point estimate for the population standard deviation is 9.72

Step by step solution

01

Step 1:Given Information

02

Step 2:Calculation

The mean of the variable is:

x¯=∑xnn=9+32+37+32+20+24+10+15+21+3010=23010=23

Now,

The formula for sample standard deviation is given below:

s=∑xi-x¯2n-1

Calculating

∑xi-x¯2

03

Step 3:Calculation (b)

Substituting 850 for∑(x-x)2

in the sampie standard deviation formulae

s=85010=94,4444=9.72

Thus, the point estimate for the population standard deviation is 9.72

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Most popular questions from this chapter

Bottlenose Dolphins. The webpage "Bottlenose Dolphin" produced by the National Geographic Society provides information about the bottlenose dolphin. A random sample of 50adult bottlenose dolphins have a mean length of 12.04ftwith a standard deviation of 1.03ft Find and interpret a 90% confidence interval for the mean length of all adult bottlenose dolphins.

Keep on Rolling. The Rolling Stones, a rock group formed in the 1960s, have toured extensively in support of new albums, Pollstar has collected data on the earnings from the Stones's North American tours. For thirty randomly selected Rolling Stones concerts, the mean gross earnings is \(2.27 million. Assuming a population standard deviation gross earnings of \)0.5 million, obtain a 99% confidence interval for the mean gross earnings of all Rolling Stones concerts. Interpret your answer in words.

Suppose that a simple random sample is taken from a normal population having a standard deviation of 10 for the purpose of obtaining a 95% confidence interval for the mean of the population.

a. If the sample size is 4 , obtain the margin of error.

b. Repeat part (a) for a sample size of 16

c. Can you guess the margin of error for a sample size of 64 ? Explain your reasoning.

American Alligators. Refer to Exercise 8.78.

a. Determine the margin of error for the 95%confidence interval.

b. Determine the margin of error for the 99%confidence interval.

c. Compare the margins of error found in parts (a) and (b).

d. What principle is being illustrated?

Corporate Farms. The U.S. Census Bureau estimates the mean value of the land and buildings per corporate farm. Those estimates are published in the Census of Agriculture, Suppose that an estimate, x, is obtained and that the margin of error is \(1000. Does this result imply that the true mean. μ, is within \)1000 of the estimate? Explain your answer.
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