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Chapter 7: Q. 7.48 (page 301)

7.48 Menopause in Mexico. In the article "Age at Menopause in Puebla. Mexico" (Human Biology, Vol. 75, No, 2, Pp. 205-206), authors L. Sievert and S. Hautaniemi compared the age of menopause for different populations. Menopause, the last menstrual period, is a universal phenomenon among females. According to the article, the mean age of menopause, surgical or natural, in Puebla, Mexico is 44.8years with a standard deviation of 5.87years. Let x~denote the mean age of menopause for a sample of females in Puebla, Mexico.
a. For samples of size 40, find the mean and standard deviation of x炉. Interpret your results in words.
b. Repeat part (a) with n=120.

Short Answer

Expert verified

(a) The mean and standard deviation for sample size 40is 44.8years and 0.928years respectively.

(b) The mean and standard deviation for sample size 120is 44.8years and 0.536 years respectively.

Step by step solution

01

Part (a) Step 1: Given information

To find the standard deviation of x, for the sample size of 40.

02

Part (a) Step 2: Explanation

Determine the standard deviation as:
蟽x炉=蟽n
The mean (渭)for the age of surgical or natural, is 44.8 years.
渭x=渭

渭x=44.8

Determine the standard deviation by substitute 5.87for 蟽and 40for nin the formula of standard deviation.

蟽x炉=蟽n
蟽x炉=5.8740
=5.876.3246
=0.928
As a result, the mean and standard deviation of all possible sample mean age of menopause, surgical or natural, are 44.8years and 0.928years, respectively, for samples of size 40 women.
03

Part (b) Step 1: Given information

To find the mean and standard deviation for sample size 120.

04

Part (b) Step 2: Explanation

Determine the standard deviation as:
蟽x炉=蟽n
The mean (渭)for the age of surgical or natural, is 44.8 years.
渭x=渭
渭x=44.8
Determine the standard deviation by substitute 5.87for 蟽and 120for nin the formula of the standard deviation.
蟽x炉=蟽n

蟽x炉=5.87120

=0.536
As a result, the mean and standard deviation of all potential sample mean age of menopause, surgical or natural, are 44.8years and 0.536 years, respectively, for samples of size 40 women.

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Most popular questions from this chapter

Population data: 1,2,3,4,5,6

Part (a): Find the mean, 渭, of the variable.

Part (b): For each of the possible sample sizes, construct a table similar to Table 7.2on the page 293and draw a dotplot for the sampling for the sampling distribution of the sample mean similar to Fig 7.1on page 293.

Part (c): Construct a graph similar to Fig 7.3and interpret your results.

Part (d): For each of the possible sample sizes, find the probability that the sample mean will equal the population mean.

Part (e): For each of the possible sample sizes, find the probability that the sampling error made in estimating the population mean by the sample mean will be 0.5or less, that is, that the absolute value of the difference between the sample mean and the population mean is at most 0.5.

Testing for Content Accuracy. A brand of water-softener salt comes in packages marked "net weight 40lb." The company that packages the salt claims that the bags contain an average of 40lbof salt and that the standard deviation of the weights is 1.5lbAssume that the weights are normally distributed.

a. Obtain the probability that the weight of one randomly selected bag of water-softener salt will be 39lb or less, if the company's claim is true.

b. Determine the probability that the mean weight of 10 randomly selected bags of water-softener salt will be 39lb or less, if the company's claim is true.

c. If you bought one bag of water-softener salt and it weighed 39lb, would you consider this evidence that the company's claim is incorrect? Explain your answer.

d. If you bought 10 bags of water-softener salt and their mean weight was 39lb, would you consider this evidence that the company's claim is incorrect? Explain your answer.

Population data: 1,2,3,4,5

Part (a): Find the mean, 渭, of the variable.

Part (b): For each of the possible sample sizes, construct a table similar to Table 7.2on the page 293and draw a dotplot for the sampling for the sampling distribution of the sample mean similar to Fig 7.1on page 293.

Part (c): Construct a graph similar to Fig 7.3and interpret your results.

Part (d): For each of the possible sample sizes, find the probability that the sample mean will equal the population mean.

Part (e): For each of the possible sample sizes, find the probability that the sampling error made in estimating the population mean by the sample mean will be 0.5or less, that is, that the absolute value of the difference between the sample mean and the population mean is at most 0.5.

Does the sample size have an effect on the mean of all possible sample means? Explain your answer.

Each years, Forbers magazine publishes a list of the richest people in the United States. As of September 16, 2013,the six richest Americans and their wealth (to the nearest billion dollars) are as shown in the following table. Consider these six people a population of interest.

Part (a): Calculate the mean wealth, 渭, of the six people.

Part (b): For samples of size 2, construct a table similar to Table 7.2 on page 293. (There are 15 possible samples of size 2.)

Part (c): Draw a dotplot for the sampling distribution of the sample mean for samples of size 2.

Part (d): For a random sample of size2, what is the chance that the sample mean will equal the population mean?

Part (e): For a random sample of size 2, determine the probability that the mean wealth of the two people obtained will be within 3 of the population mean. Interpret your result in terms of percentages.
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