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- Tardigrades, or water bears, are a type of micro-animal famous for their resilience. In examining the effects of radiation on organisms, an expert claimed that the amount of gamma radiation needed to sterilize a colony of tardigrades no longer has a mean of 900 Gy (grays). (For comparison, humans cannot withstand more than 10 Gy .) A study was conducted on a sample of 27 randomly selected tardigrade colonies, finding that the amount of gamma radiation needed to sterilize a colony had a sample mean of 907 Gy , with a sample standard deviation of 17 Gy . Assume that the population of amounts of gamma radiation needed to sterilize a colony of tardigrades is approximately normally distributed. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.05 level of significance, to support the claim that μ , the mean amount of gamma radiation needed to sterilize a colony of tardigrades, is not equal to 900…Tardigrades, or water bears, are a type of micro-animal famous for their resilience. In examining the effects of radiation on organisms, an expert claimed that the amount of gamma radiation needed to sterilize a colony of tardigrades no longer has a mean of 900 Gy (grays). (For comparison, humans cannot withstand more than 10 Gy .) A study was conducted on a sample of 27 randomly selected tardigrade colonies, finding that the amount of gamma radiation needed to sterilize a colony had a sample mean of 907 Gy , with a sample standard deviation of 17 Gy . Assume that the population of amounts of gamma radiation needed to sterilize a colony of tardigrades is approximately normally distributed. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.05 level of significance, to support the claim that μ , the mean amount of gamma radiation needed to sterilize a colony of tardigrades, is not equal to 900…A geneticist conducted a hybridization experiment with peas, which resulted in offspring consisting of 410 peas with green pods and 150 peas with yellow pods. According to Mendel’s theory, 1/4 of the offspring peas should have yellow pods. Use a 0.05 significance level to test the claim that the proportion of peas with yellow pods is equal to 0.25. Provide answers below.
- Tardigrades, or water bears, are a type of micro-animal famous for their resilience. In examining the effects of radiation on organisms, an expert claimed that the amount of gamma radiation needed to sterilize a colony of tardigrades no longer has a mean of 1350 Gy (grays). (For comparison, humans cannot withstand more than 10 Gy .) A study was conducted on a sample of 18 randomly selected tardigrade colonies, finding that the amount of gamma radiation needed to sterilize a colony had a sample mean of 1375 Gy , with a sample standard deviation of 75 Gy . Assume that the population of amounts of gamma radiation needed to sterilize a colony of tardigrades is approximately normally distributed. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.05 level of significance, to support the claim that μ , the mean amount of gamma radiation needed to sterilize a colony of tardigrades, is not equal to 1350 Gy .An analysis was conducted by the Statistics Consulting Center atVirginia Polytechnic Institute and State University in which acertain treatment was applied to a set of tree stumps. The chemicalGarlon was used the with the purpose of regenerating the roots ofthe stumps. A spray was used with four levels of GarlonPage 23 of 23concentration. After a period of time the height of the shoots wasobserved. Does the concentration of Garlon has a significantimpact on the height of the shoots? Use α = 0.05.Suppose an experiment finds that people taking a new herbal remedy get fewer colds than people taking a placebo. The results are statistically significant at the 0.01 level. Has the experiment proven that the herbal remedy works?
- In this study, the protection of aquatic ecosystems is an important goal of Ville de Montréal. In particular, Thomas wants to see whether the contamination of creeks (ruisseaux in French) by Escherichia coli differs among the months of May, June, July, and August. Therefore, he randomly samples six creeks in different areas. For each creek, he collects water samples from May to August, and measures the amount of E. coli, expressed in colony forming units (CFU) per 100 mL of water. For each combination of a month and a creek, he thus obtains an E. coli contamination value, i.e., 24 observations in total. A preliminary statistical analysis produces the following results. 13-a) Does the mean E. coli contamination differ significantly among the four months? Justify your answer to this question with the result of a statistical test. Use α = 0.05. 13-b) Which pairs of months show significant differences in mean E. coli contamination? Explain your reasoning and justify your answer…Delta has a new jumbo jet they believe will decrease the flight time from Newark to London Heathrow. To be faster than its competitors, the mean must be less than 6 h 50 minutes (or 410 minutes). Because of costs, the agency monitoring the flight times only requires that eight trials be run. The results (in minutes) are given in the spreadsheet. If the FAA requires that the agency be 90% confident of its findings (so an alpha level of 0.10), what should the agency report? Conduct an appropriate hypothesis test using Excel. Assume the population distribution is approximately normal.An article indicated that the biggest issue facing e-retailers is the ability to turn browsers into buyers. The article stated that less than 10% of browsers buy something from a particular website. A SRS of 2000 browsers was taken of which 180 made a purchase. Let alpha = .10.
- Outline the components of the classical experimental design. How is it different from a one-group pre-test post-test design?The average drying time of a manufacturer’s paint is 20 minutes. Investigating the effectiveness of a modifica-tion in the chemical composition of her paint, the manu-facturer wants to test the null hypothesis μ = 20 minutes against a suitable alternative, where μ is the average dry-ing time of the modified paint. (a) What alternative hypothesis should the manufactureruse if she does not want to make the modification in thechemical composition of the paint unless it decreases thedrying time?(b) What alternative hypothesis should the manufactureruse if the new process is actually cheaper and she wants tomake the modification unless it increases the drying timeof the paint?It is believed that a sweetener called xylitol helps prevent ear infections. In a randomized experiment, 165 children took a placebo and 68 of them got ear infections. Another sample of 159 children took xylitol and 46 of them got ear infections. The scientists believe that the proportion of ear infections in the placebo group will be greater than the xylitol group. Test this hypothesis at α = 0.025.