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Terminology Answer each of the following statements true or false regarding the level of significance a of a hypothesis test.
(i) The level of significance is the probability of rejecting the null hypothesis when it is in fact true.
(ii)The level of significance of a test depends on the value of the sample test statistic.
(iii)The level of significance is generally set in advance before samples are drawn.
(iv)The level of significance depends on the alternate hypothesis.
(v) The level of significance of a test depends on the
(i)
The statement “The level of significance is the probability of rejecting the null hypothesis when it is in fact true.” is true or false.
Answer to Problem 1CR
Solution: The statement “The level of significance is the probability of rejecting the null hypothesis when it is in fact true.” is true.
Explanation of Solution
The level of significance is the probability of rejecting the null hypothesis when it is in fact true is true. This is the probability of type I error when we reject the null hypothesis.
(ii)
The statement “The level of significance of a test depends on the value of the sample test statistic.” is true or false.
Answer to Problem 1CR
Solution: The statement “The level of significance of a test depends on the value of the sample test statistic.” is false.
Explanation of Solution
The level of significance is determined by the researcher before conducting the experiment. The significance level decides whether to reject the alternate hypothesis or not. Hence the level of significance of a test does not depend on the value of the sample test statistic.
(iii)
The statement “The level of significance is generally set in advance before samples are drawn.” is true or false.
Answer to Problem 1CR
Solution: The statement “The level of significance is generally set in advance before samples are drawn.” is true.
Explanation of Solution
The level of significance is determined by the researcher before conducting the experiment. The significance level decides whether to reject the alternate hypothesis or not. Hence the statement “The level of significance is generally set in advance before samples are drawn.” is true.
(iv)
The statement “The level of significance depends on the alternate hypothesis.” is true or false.
Answer to Problem 1CR
Solution: The statement “The level of significance depends on the alternate hypothesis” is false.
Explanation of Solution
The level of significance is determined by the researcher before conducting the experiment. The significance level decides whether to reject the alternate hypothesis or not. The statement “The level of significance depends on the alternate hypothesis” is false.
(v)
The statement “The level of significance of a test depends on the sample size.” is true or false.
Answer to Problem 1CR
Solution: The statement “The level of significance of a test depends on the sample size.” is false.
Explanation of Solution
The level of significance is determined by the researcher before conducting the experiment. The significance level decides whether to reject the alternate hypothesis or not. The statement “The level of significance of a test depends on the sample size.” is false.
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Chapter 9 Solutions
Understanding Basic Statistics
- What term is used to express the likelihood of an event occurring? Are there restrictions on its values? If so, what are they? If not, explain.arrow_forwardPopulation 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?arrow_forward
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