Confidence Intervals:
(a) Compute a 95% confidence interval for µ based on a sample of size 49. What is the value of the margin of error?
(b) Compute a 95% confidence interval for µ based on a sample of size 100. What is the value of the margin of error?
(c) Compute a 95% confidence interval for µ based on a sample of size 225. What is the value of the margin of error?
(d) Compare the margins of error for parts (a) through (c). As the sample size increases, does the margin of error decrease?
(e)Critical Thinking Compare the lengths of the confidence intervals for parts (a) through (c). As the sample size increases, does the length of a 90% confidence interval decrease?
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Understanding Basic Statistics
- 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?arrow_forwardCONFIDENCE INTERVAL AND THE CENTRAL LIMIT THEOREM 1. A nutritionist is interested in monitoring the calorie intake of woman. It was found that in selected a random sample of 50 female adults, the average daily intake of meat products is 2200 calories per day with the standard deviation of 300 calories. Give a 99% confidence interval for the mean intake of calories from meat products of female adults. 2.Give a 90%, 95% and 99% confidence interval of the mean weight of fresh orange if 100 randomly selected fresh orange have a mean weight of 180 grams and standard deviation f 30g (3 answers)arrow_forwardFinding Confidence Intervals. , Assume that each sample is a simple random sample obtained from a population with a normal distribution. a. Comparing Waiting Lines The values listed below are waiting times (in minutes) of customers at the Jefferson Valley Bank, where customers enter a single waiting line that feeds three teller windows. Construct a 95% confidence interval for the population standard deviation σ. 6.5 6.6 6.7 6.8 7.1 7.3 7.4 7.7 7.7 7.7 b. The values listed below are waiting times (in minutes) of customers at the Bank of Providence, where customers may enter any one of three different lines that have formed at three teller windows. Construct a 95% confidence interval for the population standard deviation σ. 4.2 5.4 5.8 6.2 6.7 7.7 7.7 8.5 9.3 10.0 c. Interpret the results found in parts (a) and (b). Do the confidence intervals suggest a difference in the variation among waiting times? Which arrangement seems better: the single-line system or the multiple-line system?arrow_forward
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