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Chapter 7: Q3 (page 339)

Last Digit Analysis The dotplot below depicts the last digits of the weights of 153 males inData Set 1 鈥淏ody Data.鈥� 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

Expert verified

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

Step by step solution

01

Given information

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

02

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.

03

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蟽.

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 蟽 cannot be estimated for the given population of the last digits.

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Most popular questions from this chapter

In Exercises 5鈥�8, use the relatively small number of given bootstrap samples to construct the confidence interval.Seating Choice In a 3M Privacy Filters poll, respondents were asked to identify their favourite seat when they fly, and the results include these responses: window, window, other, other. Letting 鈥渨indow鈥� = 1 and letting 鈥渙ther鈥� = 0, here are ten bootstrap samples for those responses: {0, 0, 0, 0}, {0, 1, 0, 0}, {0, 1, 0, 1}, {0, 0, 1, 0}, {1, 1, 1, 0}, {0, 1, 1, 0}, {1, 0, 0, 1}, {0, 1, 1, 1}, {1, 0, 1, 0}, {1, 0, 0, 1}. Using only the ten given bootstrap samples, construct an 80% confidence interval estimate of the proportion of respondents who indicated their favourite seat is 鈥渨indow.鈥�

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a. Assume that nothing is known about the percentage of passengers who prefer aisle seats.

b. Assume that a prior survey suggests that about 38% of air passengers prefer an aisle seat

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a. What is the number of degrees of freedom that should be used for finding the critical value t伪2?

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