Question

Last Digit Analysis The dotplot below depicts the last digits of the weights of 153 males inData Set 1 “Body Data.” Do those digits appear to be from a normally distributed population? If not, does the large sample size ofn= 153 justify treating the values as if they were from a normal distribution? Can the sample be used to construct a 95% confidence interval estimate of for the population of all such digits?

Short answer

No, the given sample cannot be used to construct a 95% confidence interval estimate of $\sigma$ for the population of all last digits of the weights of males.

Step-by-step solution

Given information

A dot plot representing the last digits of weights of 153 males is provided. A 95% confidence interval estimate of $\sigma$ is to be constructed.

Analysis of the population distribution from the dotplot

The given dotplot represents the last digits of weights of a sample of 153 males.

If the dotplot appears to be bell-shaped, the distribution of the population from which the sample is taken is said to be normal.

Here, the dotplot is far from being bell-shaped.

Thus, the population of the last digits of weights from which the sample is extracted is not normally distributed.

Requirement of Interval Estimation of  σ

The requirement of the population to be strictly normally distributed, even if the sample size is large, is extremely stringent in order to obtain the confidence interval estimate of$\sigma$.

Although the sample of the last digits is of a large size (153), the population of the last digits is not normally distributed.

Therefore, the 95% confidence of $\sigma$ cannot be estimated for the given population of the last digits.