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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

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.

In Exercises 13鈥�20, use the data in the table below for sitting adult males and females (based on anthropometric survey data from Gordon, Churchill, et al.). These data are used often in the design of different seats, including aircraft seats, train seats, theatre seats, and classroom seats. (Hint: Draw a graph in each case.)

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23.5 in

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Find the probability that a male has a back-to-knee length between 22.0 in. and 24.0 in.

Low Birth Weight The University of Maryland Medical Center considers 鈥渓ow birth weights鈥� to be those that are less than 5.5 lb or 2495 g. Birth weights are normally distributed with a mean of 3152.0 g and a standard deviation of 693.4 g (based on Data Set 4 鈥淏irths鈥� in Appendix B).

a. If a birth weight is randomly selected, what is the probability that it is a 鈥渓ow birth weight鈥�?

b. Find the weights considered to be significantly low, using the criterion of a birth weight having a probability of 0.05 or less.

c. Compare the results from parts (a) and (b).

Finding Bone Density Scores. In Exercises 37鈥�40 assume that a randomly selected subject is given a bone density test. Bone density 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 bone density test score corresponding to the given information. Round results to two decimal places.

Find the bone density scores that can be used as cutoff values separating the lowest 3% and highest 3%.

Redesign of Ejection SeatsWhen women were finally allowed to become pilotsoffighter jets, engineers needed to redesign the ejection seats because they had been originallydesigned for men only. The ACES-II ejection seats were designed for men weighing between

140 lb and 211 lb. Weights of women are now normally distributed with a mean of 171 lb and astandard deviation of 46 lb (based on Data Set 1 鈥淏ody Data鈥滱ppendix B).

a.If 1 woman is randomly selected, find the probability that her weight is between 140 lb and 211 lb.

b.If 25 different women are randomly selected, find the probability that their mean weight is between 140 lb and 211 lb.

c.When redesigning the fighter jet ejection seats to better accommodate women, which probability is more relevant: the result from part (a) or the result from part (b)? Why?
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