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Chapter 6: Q7E (page 339)

Explain the difference between an interval estimator and a point estimator for 渭

Short Answer

Expert verified

A random variable is an estimator, as well as a value, is an estimation that represents the estimator's calculated number.

Step by step solution

01

Interval estimation

In comparison to point estimate, which is a specific number, interval estimation uses sample information to determine a range of potential (as well as likely) numbers for an unbiased estimator.

02

Difference between interval estimator and point estimator

A point estimatoris a single data point computed from the sampling that predicts a targeted population variable.

A population variable point estimate is a technique as well as an equation that informs us how to utilize sampling information to construct a specific figure that may be used as a goal variable estimation.

An interval estimator(also known as a confidence level) is a method that informs us on how to generate an interval that predicts the targeted variable using data samples.

The two types of population parameter estimates depending on sampling information are point as well as interval estimations. The point estimate is a simple process. The interval estimate, on the other hand, is a considerably more reliable as well as useful technique than the point estimates.

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Most popular questions from this chapter

It costs you \(10 to draw a sample of size n = 1 and measure the attribute of interest. You have a budget of \)1,500.

a. Do you have sufficient funds to estimate the population mean for the attribute of interest with a 95% confidence interval 5 units in width? Assume蟽=14.

b. If you used a 90% confidence level, would your answer to part a change? Explain.

FindZ伪/2for each of the following:

a.= .10

b.= .01

c.= .05

d.= .20

Surface roughness of pipe. Refer to the Anti-corrosion Methods and Materials (Vol. 50, 2003) study of the surface roughness of coated interior pipe used in oil fields, Exercise 2.46 (p. 96). The data (in micrometers) for sampled pipe sections are reproduced in the accompanying table; a Minitab analysis of the data appears below.

a.Locate a 95%confidence interval for the mean surface roughness of coated interior pipe on the accompanying Minitab printout.

b.Would you expect the average surface roughness to beas high as 2.5micrometres? Explain.

Suppose you have selected a random sample of n = 5 measurements from a normal distribution. Compare the standard normal z-values with the corresponding t-values if you were forming the following confidence intervals.

a. 80% confidence interval

b. 90% confidence interval

c. 95% confidence interval

d. 98% confidence interval

e. 99% confidence interval

f. Use the table values you obtained in parts a鈥揺 to sketch the z- and t-distributions. What are the similarities and differences?

Lobster trap placement. An observational study of teams fishing for the red spiny lobster in Baja California Sur, Mexico, was conducted and the results published in Bulletin of Marine Science(April 2010). One of the variables of interest was the average distance separating traps鈥攃alled trap spacing鈥攄eployed by the same team of fishermen. Trap-spacing measurements (in meters) for a sample of seven teams of red spiny lobster fishermen are shown in the accompanying table. Of interest is the mean

trap spacing for the population of red spiny lobster fishermen fishing in Baja California Sur, Mexico.

93

99

105

94

82

70

86

  1. Identify the target parameter for this study.
  2. Compute a point estimate of the target parameter.
  3. What is the problem with using the normal (z) statistic to find a confidence interval for the target parameter?
  4. Find a 95% confidence interval for the target parameter.
  5. Give a practical interpretation of the interval, part d.
  6. What conditions must be satisfied for the interval, part d, to be valid?
See all solutions

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