(a) Explanation The characteristics of the sampling distribution x ¯ , for all the sample size n is determined using the central limit theorem. Based on central limit theorem the sample size n must be greater than or equal to 30 for making the distribution of sample means x (b) To determine Identify whether it is necessary to make any restrictions about sample size for claiming that the distribution of sample means x ¯ taken from random samples of a given size is normal, if the original distribution of x values is known to be normal.

Understandable Statistics: Concepts and Methods

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ISBN: 9781337119917

Author: Charles Henry Brase, Corrinne Pellillo Brase

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Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 6.5, Problem 7P

(a)

To determine

Mention the sample size that is required to claim that the distribution of sample means x¯ to be approximately normal.

(b)

To determine

Identify whether it is necessary to make any restrictions about sample size for claiming that the distribution of sample means x¯ taken from random samples of a given size is normal, if the original distribution of x values is known to be normal.

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Understandable Statistics: Concepts and Methods

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Population Genetics In the study of population genetics, an important measure of inbreeding is the proportion of homozygous genotypesthat is, instances in which the two alleles carried at a particular site on an individuals chromosomes are both the same. For population in which blood-related individual mate, them is a higher than expected frequency of homozygous individuals. Examples of such populations include endangered or rare species, selectively bred breeds, and isolated populations. in general. the frequency of homozygous children from mating of blood-related parents is greater than that for children from unrelated parents Measured over a large number of generations, the proportion of heterozygous genotypesthat is, nonhomozygous genotypeschanges by a constant factor 1 from generation to generation. The factor 1 is a number between 0 and 1. If 1=0.75, for example then the proportion of heterozygous individuals in the population decreases by 25 in each generation In this case, after 10 generations, the proportion of heterozygous individuals in the population decreases by 94.37, since 0.7510=0.0563, or 5.63. In other words, 94.37 of the population is homozygous. For specific types of matings, the proportion of heterozygous genotypes can be related to that of previous generations and is found from an equation. For mating between siblings 1 can be determined as the largest value of for which 2=12+14. This equation comes from carefully accounting for the genotypes for the present generation the 2 term in terms of those previous two generations represented by for the parents generation and by the constant term of the grandparents generation. a Find both solutions to the quadratic equation above and identify which is 1 use a horizontal span of 1 to 1 in this exercise and the following exercise. b After 5 generations, what proportion of the population will be homozygous? c After 20 generations, what proportion of the population will be homozygous?

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Mention the sample size that is required to claim that the distribution of sample means x ¯ to be approximately normal.

Solution Summary: The author explains the sample size that is required to claim that the distribution of sample is approximately normal, even if the population is not normally distributed.

Mention the sample size that is required to claim that the distribution of sample means x¯ to be approximately normal.

Identify whether it is necessary to make any restrictions about sample size for claiming that the distribution of sample means x¯ taken from random samples of a given size is normal, if the original distribution of x values is known to be normal.

Chapter 6 Solutions