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Chapter 7: Problem 105

Suppose that, when taking a random sample of 4 from 123 women, you get a mean height of only 60 inches ( 5 feet). The procedure may have been biased. What else could have caused this small mean?

Short Answer

Expert verified
Possible causes for this small mean could be bias in the sampling procedure, errors in data collection, small sample size, specific characteristics of the sample population, or external factors affecting height.

Step by step solution

01

Identify Sampling Procedure

The first step is to consider if there may have been a bias in the sampling procedure. Bias can occur if the sample is not truly random, which may result in an unrepresentative sample. This means that the women who ended up in the sample may be distinct in their heights compared to the general population of 123 women.
02

Analyze the Data Collection Method

Analyze if there may have been a mistake or error in the height measurements. This could be a result of a faulty measuring device, incorrect recording, or misunderstanding of the units of measurement.
03

Consider the Sample Size

Given that the sample size is only 4, it's possible that this small sample size may result in a non-representative average height. A larger sample size generally provides a better estimate of the population mean.
04

Understand the Population Sample

Consider if there may be a specific characteristic of the population sampled. For example, if the sample of 123 women were from a specific region, occupation, age group, etc., they might inherently have shorter average heights than the general population.
05

Consider External Factors

Finally, consider if there were any external factors that might have affected the heights of the women in the sample, such as nutritional factors or health conditions.

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Most popular questions from this chapter

The website www.mlb.com compiles statistics on all professional baseball players. For the 2017 season, statistics were recorded for all 663 players. Of this population, the mean batting average was \(0.236\) with a standard deviation of \(0.064\). Would it be appropriate to use this data to construct a \(95 \%\) confidence interval for the mean batting average of professional baseball players for the 2017 season? If so, construct the interval. If not, explain why it would be inappropriate to do so.

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