Essay on Data analysis. Paper must be at least 1500 words. (iv) In a random sample of 100 students at a particular university, 60 indicated that they favoured having the option of receiving pass-fail grade for elective courses. Obtain a 90% confidence interval for the proportion of the population of students who favour pass-fail grades for elective courses. Does this confidence interval contain the value? Explain why this particular value might be of interest.(i) Suppose 16 tax returns are randomly sampled by the Australian Taxation Office from the population of 1987 tax returns with adjusted gross income between $25000 and $30000. The interest deductions (in $) claimed on the returns are as follows:In 1980 the average interest deductions for individuals in this tax bracket was $3011. Do the sample data provide sufficient evidence to conclude that in 1987 the average interest deduction claimed by taxpayers in this income bracket was different from 1980? Use. State all the assumptions you need to perform the test.Assuming that the sample comes from a normal population. Since, the population standard deviation is unknown, therefore using t-distribution to perform the test. The hypothesis test will one sample mean vs. hypothesized value two tail test.(ii) An economist claims that the unemployment rate for non-English speaking individuals in New York City is at least 30%. In a random sample of 400 non-English speaking residents of New York City, 90 are unemployed.(iii) Twenty babies are randomly selected for an experiment to determine if different brands of baby food affect a childs weight. The babies are separated into 5 groups, and each group is fed a different diet. The weight gained in pounds by each baby after being on the diet four months is recorded in the following table:Use a 1% level of significance level to test if the type of diet affects weight gain. Clearly state the null and alternative hypotheses and state all the necessary assumptions
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