Describe the term 'controlled selection'.
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- The culinary herb cilantro, Coriandrum sativum, is very polarizing: some people love it and others hate it. A genetic component is suspected in this phenomenon. A survey of American adults of European ancestry found that 1129 of 7295 women and 865 of 7309 men said that cilantro tastes soapy. We want to know if women and men in this population differ in how they perceive the taste of cilantro. What is the pooled sample proportion of women and men who say that cilantro tastes soapy? Conduct a hypothesis test, and state the test statistic and p-value and give the conclusion. How much differ? Construct a 95% confidence interval for the difference of the proportions of women and men who say that cilantro tastes soapy. Interpret your interval in the context.Currently, studies are being done on whether one COVID vaccine (like Pfizer’s) can be mixed and matched with another COVID vaccine (like Moderna’s). So a person could have the first shot of one and the second shot of the other. Let’s say a study was done to try to determine if mixing and matching is as effective as just using one type for both shots. People show up at a clinic on a Saturday (self-selecting), and are first given the Pfizer vaccine, and then the Moderna vaccine 3 weeks later. Suppose the results showed that only 1% of all of the people got COVID. What is a problem with this study? A) There was no random assignment of participants to groups. B) It is observational, and an experiment would have been better due to the potential of confounding. C) There was no control group, i.e. a group to compare the results to. D) All of the above3) Suppose you wish to perform model selection in multiple regression, but your statistical program can only fit individual multiple regression models, and does not do best subset selection, stepwise selection, or backward selection. Which of these three model selection procedures will be easiest to implement by fitting a series of individual multiple regression models? Briefly explain how you would implement one of these three model selection procedures by fitting individual multiple regression models.
- A particular industrial product is shipped in lots of 20 items per lot. Testing to determine whether an item is defective is costly, and hence the manufac- turer samples his production rather than using a 100% inspection plan. A sampling plan constructed to minimize the number of defective shipped to customers calls for sampling 5 items from each lot and rejecting the lot if more than 1 defective is ob- served. It is believed that 10% of lots contains 3 defectives, 20% contains 2 defectives, 30% contains 1 defective and 40% contains no defectives. If a randomly accepted lot has one defective in the sample, what is the probability that the accepted lot still contains at least one defective? (А) 0.375 (В) 0.475 (C) 0.525 (D) 0.625 (E) 0.775As products come off a large assembly line, they are inspected for quality. They are placed into one of three categories: pass, fail, or need additional inspection. The manager claims that 80% of the products pass the inspection, 5% fail, and 15% need additional inspection. In an effort to increase the passing rate, the machines are recalibrated. After this recalibration, a random sample of 100 products is selected. It is discovered that 85 passed inspection, 2 failed, and 13 needed additional inspection. The manager would like to know if there is convincing evidence that the distribution has changed. What is the value of the chi-square test statistic and P-value? Find the chi-square table here. χ2 = 2.38, P-value is less than 0.0005 χ2 = 2.38, P-value is greater than 0.25 χ2 = 5.10, P-value is less than 0.0005 χ2 = 5.10, P-value is greater than 0.25A crop researcher investigated the phenotypes that resulted from crossing two different types of cucumber plants. There are 4 possible resulting phenotypes (numbered 1, 2, 3, 4 in the data table below). Mendel's laws of genetic inheritance ('the model') suggest that the proportions should be 9/16, 3/16, 3/16 and 1/16 for phenotypes 1, 2, 3, 4 respectively. The classification of a sample of 1400 observations is given below together with the proportions suggested by Mendel's laws of inheritance (the model). Give the degrees of freedom that would be used in a test of whether or not the crossing results in a population that follows Mendel's laws of inheritance. Degrees of freedom =
- Sickle-cell anemia is a hereditary chronic blood disease that is extremely severe when an individual carries two copies of the defective gene. It is particularly common in countries plagued by malaria, a parasiticinfection transmitted by mosquitoes. A study in Africa tested 543 children for the sickle-cell gene and also for malaria. In Group 1 which consisted of 136 children with the sickle-cell gene, 36 children had severe malariainfections. Group 2 consisted of 407 children without the sickle-cell gene, and 152 of them had severe malaria infections. Conduct a test to determine if the proportion of severe malaria infections among children withthe sickle-cell trait is different from that among children without. Test at 5% level of significance. Question: What is your p value and t statistic ?Assortative mating is a nonrandom mating pattern where individuals with similar genotypes and/or phenotypes mate with one another more frequently than what would be expected under a random mating pattern. Researchers studied this topic and collected data on Scandinavian men and their female partners. They found out 60% of Scandinavian men have blue eyes. Among those men with blue eyes, 80% of them choose female partners with blue eyes. Among those Scandinavian men whose eye color is not blue, 20% of them have partners with blue eyes. Given that a man’s partner has blue eyes, what’s that probability this man has blue eyes? If 60% of Scandinavian men have blue eyes and you randomly select 8 men, what’s the probability that none of them has blue eyes?
