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Chapter 6: Q3 (page 263)

Unbiased Estimators Data Set 4 鈥淏irths鈥� in Appendix B includes birth weights of 400 babies. If we compute the values of sample statistics from that sample, which of the following statistics are unbiased estimators of the corresponding population parameters: sample mean; sample median; sample range; sample variance; sample standard deviation; sample proportion?

Short Answer

Expert verified

Out of the given statistics, the sample mean, the sample variance, and the sample proportion are unbiased estimators of the corresponding population parameters.

Step by step solution

01

Given information

A sample of 400 birth weights is selected, and the sample statistics are computed.

02

Unbiased estimators

An unbiased estimator is a sample statistic when the sampling distribution of the statistic has a mean value equal to the corresponding population parameter.

It is known that the following statistics are unbiased estimators of their corresponding population parameters:

  • Sample proportion
  • Sample mean
  • Sample variance

In addition, the following statistics are biased estimators of their population parameters:

  • Sample median
  • Sample range
  • Sample standard deviation

Therefore, out of the given statistics, the sample mean, the sample variance, and the sample proportion are unbiased estimators of the corresponding population parameters.

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Most popular questions from this chapter

Water Taxi SafetyWhen a water taxi sank in Baltimore鈥檚 Inner Harbor, an investigation revealed that the safe passenger load for the water taxi was 3500 lb. It was also noted that the mean weight of a passenger was assumed to be 140 lb. Assume a 鈥渨orst-case鈥� scenario in which all of

the passengers are adult men. Assume that weights of men are normally distributed with a mean of 188.6 lb and a standard deviation of 38.9 lb (based on Data Set 1 鈥淏ody Data鈥� in Appendix B).

a. If one man is randomly selected, find the probability that he weighs less than 174 lb (the new value suggested by the National Transportation and Safety Board).

b. With a load limit of 3500 lb, how many male passengers are allowed if we assume a mean weight of 140 lb?

c. With a load limit of 3500 lb, how many male passengers are allowed if we assume the updated mean weight of 188.6 lb?

d. Why is it necessary to periodically review and revise the number of passengers that are allowed to board?

Random Digits Computers are commonly used to randomly generate digits of telephone numbers to be called when conducting a survey. Can the methods of this section be used to find the probability that when one digit is randomly generated, it is less than 3? Why or why not? What is the probability of getting a digit less than 3?

Using a Formula to Describe a Sampling Distribution Exercise 15 鈥淏irths鈥� requires the construction of a table that describes the sampling distribution of the proportions of girls from two births. Consider the formula shown here, and evaluate that formula using sample proportions (represented by x) of 0, 0.5, and 1. Based on the results, does the formula describe the sampling distribution? Why or why not?

Px=122-2x!2x!wherex=0,0.5,1

In Exercises 9鈥�12, find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.

Standard Normal DistributionIn Exercises 17鈥�36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of the given bone density test scores. If using technology instead of Table A-2, round answers

to four decimal places.

Between -3.00 and 3.00.
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