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- The United States Bureau of Labor Statistics (BLS) conducts the Quarterly Census of Employment and Wages (QCEW) and reports a variety of information on each county in America. In the third quarter of 2016, the QCEW reported the total taxable earnings, in millions, of all wage earners in all 3222 counties in America. Suppose that James is an economist who collects a simple random sample of the total taxable earnings of workers in 52 American counties during the third quarter of 2016. According to the QCEW, the true population mean and standard deviation of taxable earnings, in millions of dollars, by county are μ=28.29 and σ=33.493, respectively. Let ?X be the total taxable earnings, in millions, of all wage earners in a county. The mean total taxable earnings of all wage earners in a county across all the counties in James' sample is x¯. Use the central limit theorem (CLT) to determine the probability ? that the mean taxable wages in James' sample of 52 counties will be less than $29…Some researchers have conjectured that stem-pitting disease in peach tree seedlings might be controlled with weed and sol treatment. An experiment was conducted to compare peach tree seedling growth with sol and weeds treated with one of two herbicides. In a field containing 20 seedlings, 10 were randomly selected from throughout the field and assigned to receive Herbicide A The remaining 10 seedlings were to receive Herbicide B. Soil and weeds for each seedling were treated with the appropriate herbicide and at the end of the study period the height (in centimeters) was recorded for each seedling. A box plot of each data set showed no indication of non-Normality. The following results were obtained: x (cm) s (cm) Herbicide A 945 10 Herbicide B 109.1 A 95% confidence interval for ug - Ha is given by which of the following expressions? (Use the conservative value for degrees of freedom) (109 1-94 5) t1 96 (109 1-94 5) + 2 263 109 1- 94 5)2196, . (109 1- 945)2262, (109 1- 94 5)2. In a population it is estimated that 20% have a desired trait of interest for the researcher. The researcher wants to know how many people on average he has to draw from a population to get 2 people with the trait. Use rows 20-24 of the Random Number Table to carry out the simulation. Explain clearly how you set up the problem and report your findings. Answer:
- A 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 =The improved crop varieties are evaluated at farmers fields before their release for a large scale production. The claim made by a chickpea breeder is that, on average, her improved variety produces higher yield of chickpea compared to the local variety grown by farmers in her region. To examine her claim, the improved variety of chickpea was evaluated at 25 randomly selected farmer-fields (farms) in that region. Each field was divided into two parts, one part of the field was randomly assigned to the improved variety to be grown under a crop management practice recommended for this variety, and the other part to the local variety with an ongoing practice followed for it. You may note there were 25 different fields and the two varieties were grown within each of them. The chickpea yields of the two varieties were measured, in kg per hectare, from each of the fields. The following R- code outputs contain the information that you may use to answer the questions. The data vectors,…A 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 = The test is carried out at significance level α = 0.05 using the method described in the lecture notes. If the decision is to not reject the null hypothesis, what is the appropriate conclusion for the test? Select the appropriate conclusion from the list below. There is sufficient evidence at α = 0.05 that…
- An agronomist is interested in comparing the efficacy of two fumigants (A and B) and a control (O) in eliminating wireworms. A field is divided into 4 sections, each section containing 3 plots. Fumigant A, B and O were randomly assigned to one plot within each section. The number of wireworms that remained on each plot after application of fumigant was recorded. Give a possible RCBD layout for the experiment.Some researchers have conjectured that stem-pitting disease in peach tree seedlings might be controlled with weed and soil treatment. An experiment was conducted to compare peach tree seedling growth with soil and weeds treated with one of two herbicides. In a field containing 20 seedlings, 10 were randomly selected from throughout the field and assigned to receive Herbicide A. The remaining 10 seedlings were to receive Herbicide B. Soil and weeds for each seedling were treated with the appropriate herbicide and at the end of the study period the height (in centimeters) was recorded for each seedling. A box plot of each data set showed no indication of non-Normality. The following results were obtained: (cm) s (cm) Herbicide A Herbicide B 94.5 109.1 10 A 95% confidence interval for uB - HA is given by which of the following expressions? (Use the conservative value for degrees of freedom.) 102 9? (109.1- 94.5) t 1.96. 102 92 (109.1- 94.5) + 2.262. 9 10 (109.1- 94.5) + 1.96, 10 V 10 102…A candy maker offers Child and Adult bags of jelly beans with different color mixes. The company claims that the Child mix has 30% red jelly beans, while the Adult mix contains 15% red jelly beans. Assume that the candy maker’s claim is true. Suppose we take a random sample of 50 jelly beans from the Child mixand a separate random sample of 100 jelly beans from the Adult mix. Let ?^ and ?^ be the sample ??proportions of red jelly beans from the Child and Adult mixes, respectively.a. What is the shape of the sampling distribution of ?^ − ?^ ? Why???b. Find the mean of the sampling distribution. Show your work.c. Find the standard deviation of the sampling distribution. Show your work.
- The United States Bureau of Labor Statistics (BLS) conducts the Quarterly Census of Employment and Wages (QCEW) and reports a variety of information on each county in America. In the third quarter of 2016, the QCEW reported the total taxable earnings, in millions, of all wage earners in all 3222 counties in America. Suppose that James is an economist who collects a simple random sample of the total taxable earnings of workers in 56 American counties during the third quarter of 2016. According to the QCEW, the true population mean and standard deviation of taxable earnings, in millions of dollars, by county are ?=28.29 and ?=33.493 , respectively. Let ? be the total taxable earnings, in millions, of all wage earners in a county. The mean total taxable earnings of all wage earners in a county across all the counties in James' sample is ?⎯⎯⎯ . Use the central limit theorem (CLT) to determine the probability ? that the mean taxable wages in James' sample of 56 counties will be less than…A researcher randomly selected 158 personal vehicles and noted the type of vehicle and its color. The two-way table displays the data. A 5-column table with 4 rows. Column 1 has entries sedan, S U V, convertible, total. Column 2 is labeled Red with entries 14, 9, 20, 43. Column 3 is labeled Blue/Green with entries 31, 19, 6, 56. Column 4 is labeled Black/Gray with entries 22, 34, 3, 59. Column 5 is labeled Total with entries 67, 62, 29, 158. The columns are titled Vehicle color and the rows are titled vehicle type. Suppose a vehicle is randomly selected. Let event C = convertible and R = red. What is the value of P(R|C)? StartFraction 29 Over 158 EndFraction StartFraction 43 Over 158 EndFraction StartFraction 20 Over 43 EndFraction StartFraction 20 Over 29 EndFraction
