Finding Critical Values and Confidence Intervals. In Exercises 5–8, use the given information to find the number of degrees of freedom, the critical values
5. Nicotine in Menthol Cigarettes 95% confidence; n = 25, s = 0.24 mg.
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ELEMENTARY STAT.(LL)-W/GDE.WKBK.+MYSTAT
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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?arrow_forwardA sample mean, sample standard deviation, and sample size are given. Use the one-mean t-test to perform the required hypothesis test about the mean, μ, of the population from which the sample was drawn. Use the critical-value approach. Sample mean = 7.1 s = 2.3 n = 18 α = 0.01 H0: µ = 10 H1: µ < 10 The critical value(s) is/are (If there are two critical values separate each with a comma and list from smallest to largest)arrow_forwardTest the claim that the proportion of men who own cats is significantly different than 50% at the 0.02 significance level.a.) The null and alternative hypothesis would be: b.) The test is: right-tailed left-tailed two-tailed Based on a sample of 60 men, 59% owned cats c.) The sample proportion ˆp=d.) The test statistic is: (to 2 decimals)e.) At α=α=0.02, the critical value is:± (to 2 decimals)f.) Based on this we: Reject the null hypothesis Fail to reject the null hypothesisarrow_forward
- Information about a random sample is given. Verify that the sample is large enough to use it to construct a confidence interval for the population proportion. Then construct a 98% confidence interval for the population proportion. (Round your answers to 4 d.p, and use the critical value for t or the t-table) a. n=80, p= 0.4 b. n=325, p= 0.4arrow_forwardA. Use the given information to find the number of degrees of freedom, the critical values χ2L and χ2R, and the confidence interval estimate of σ. It is reasonable to assume that a simple random sample has been selected from a population with a normal distribution. Platelet Counts of Women 90% confidence; n=21, s=65.6.arrow_forwardRandom samples of size 100 are taken from an infinite population whose population proportion is 0.2. The expected value and standard error of the sample proportion are A) 20 and .04 B) 0.2 and 0.2 C) 20 and 0.2 D) 0.2 and .04arrow_forward
- Test the claim that the mean GPA of night students is significantly different than the mean GPA of day students at the 0.05 significance level. The sample consisted of 30 night students, with a sample mean GPA of 3.07 and a standard deviation of 0.05, and 20 day students, with a sample mean GPA of 3.06 and a standard deviation of 0.03. The test statistic is: (to 2 decimals)The positive critical value is: (to 2 decimals)arrow_forwardtest the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Cardiac Arrest at Day and Night A study investigated survival rates for in-hospital patients who suffered cardiac arrest. Among 58,593 patients who had cardiac arrest during the day, 11,604 survived and were discharged. Among 28,155 patients who suffered cardiac arrest at night, 4139 survived and were discharged (based on data from “Survival from In-Hospital Cardiac Arrest During Nights and Weekends,” by Peberdy et al., Journal of the American Medical Association, Vol. 299, No. 7). We want to use a 0.01 significance level to test the claim that the survival rates are the same for day and night. a. Test the claim using a hypothesis test. b. Test the claim by constructing an appropriate confidence interval. c. Based on the results, does it appear that for in-hospital patients…arrow_forwardTest the claim that the mean GPA of night students is significantly different than the mean GPA of day students at the 0.02 significance level. The sample consisted of 30 night students, with a sample mean GPA of 2.67 and a standard deviation of 0.02, and 65 day students, with a sample mean GPA of 2.62 and a standard deviation of 0.05.The test statistic is: ________________ (to 2 decimals)The positive critical value is: _________________ (to 2 decimals)Based on this we: Reject the null hypothesis Fail to reject the null hypothesisarrow_forward
- Mean Pulse Rate of Females Data Set 1 “Body Data” in Appendix B includes pulse rates of 147 randomly selected adult females, and those pulse rates vary from a low of 36 bpm to a high of 104 bpm. Find the minimum sample size required to estimate the mean pulse rate of adult females. Assume that we want 99% confidence that the sample mean is within 2 bpm of the population mean. a. Find the sample size using the range rule of thumb to estimate b. Assume that σ = 12.5 bpm, based on the value of s = 12.5 bpm for the sample of 147 female pulse rates. c. Compare the results from parts (a) and (b). Which result is likely to be better?arrow_forwardTest the claim that the proportion of children in the high income group that drew the nickel too large is smaller than 50%. Test at the 0.05 significance level.a) Identify the correct alternative hypothesis: μ>.50μ>.50 p<.50p<.50 p>.50p>.50 p=.50p=.50 μ<.50μ<.50 μ=.50μ=.50 Give all answers correct to 3 decimal places.b) The test statistic value is: c) Using the P-value method, the P-value is: d) Based on this, we Reject H0H0 Fail to reject H0H0 e) Which means There is sufficient evidence to warrant rejection of the claim There is not sufficient evidence to support the claim There is not sufficient evidence to warrant rejection of the claim The sample data supports the claimarrow_forwardUse the Chi-Square test to determine if your third-generation population data fits the expected population. Show all calculations and state the P-value you obtain (use p and q numbers from generation 0 and 3 in the calculation). Generation 0 number for p = .5 and Q = .5 Generation 3 number for P= .6 and Q = .4arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning