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Statistical Methods for Management II Semester 402 Assignment 1 Question # 1. A survey of CPAs across the United States found that the average net income for sole proprietor CPAs is $74,914. Because this survey is now more than 15 years old, as accounting researcher wants to test this figure by taking a random sample 112 sole proprietor accountants in the United States to determine whether the net income figure changes and sample mean is $78695. The researcher could use the seven steps of hypothesis testing to do so. Assume the population standard deviation of net incomes for sole proprietor CPAs is $14530. Using a level of significance of 0.05 test. Question # 2. The U.S. Farmers' Production Company build large harvesters. For a harvester to be properly balanced when operating, a 25-pound plate is installed on its side. The machine that produces these plates is set to yield plates that averages 25 pounds. The distribution of plates produced from the machine is normal. However, the shop supervisor is worried that the machine is out of adjustment and is producing plates that do not average 25 pounds. The test this concern, he randomly selects 20 of the plates produced the day before and weights them. Following table shows the weights obtained, along with the computed sample mean and ample standard deviation. 22.6 22.2 23.2 27.4 24.5 27 26.6 28.1 26.9 24.9 26.2 25.3 23.1 24.2 26.1 25.8 30.4 28.6 23.5 23.6 x=355, s=2.1933, n=20 The test is to determine whether the machine is out of control, and the shop supervisor has not specified whether he believes the machine is producing plates that too heavy or too light. Assume α = 0.05. Question # 3. A survey of the morning beverage market shows that the primary breakfast beverage for 17% of Saudi Arabia is milk. A mild producer in Jubail, where milk is plentiful, believes the figure is higher for Jubail. To test this idea, he contacts a random sample of 550 Jubail residents and asks which primary beverage they consumed for breakfast that day. Suppose 115 replied that milk was the primary beverage. Using a level of significance of 0.05 test the idea that the milk figure is higher for Jubail. Question # 4. A Washington Post-ABC News poll found that 72% of people are concerned about the possibility that their personal records could be stolen over the Internet. If a random sample of 300 college students at a Midwestern university were taken and 228 of them were concerned about the possibility that their personal records could be stolen over the Internet, could you conclude at the 0.025 level of significance that a higher proportion of the university's college students are concerned about Internet theft than the public at large? Report the p-value for this test.
Adi S.
STA3024: INTRO TO STATISTICS 2, Spring 2018 2. Epidemiologists want to determine if there is an association between region and type of malaria infections. They randomly collect data from Asia, Africa, and South America on the counts of individuals who were infected by four kinds of malaria parasites (labeled as A-D instead of by their scientific name). The data is summarized below. Region Parasite Asia Africa South America Total Malaria A 31 14 45 90 Malaria B 10 5 62 77 Malaria C 53 45 8 106 Malaria D 20 72 12 104 Total 114 136 127 377 (a) State the hypotheses for a chi-squared test for independence. (b) Compute the test statistic X". (c) Based on the X" and the chi-squared table, determine what figure the p-value is less than and state the conclusion of the chi-squared test for independence. (d) Using region as the explanatory variable, complete the table of conditional probabilities of type of malaria infection given region. (e) What conclusions can we draw about the association between region and kinds of malaria infections? Be specific about the likelihood of getting which types of malaria infections based on which regions, and make sure to comment on all 4 types. (f) There is clearly a strong relationship between region and type of malaria infection. Is this because the X" statistic in part (b) is large? Explain your answer. 3. A focus group is interested in studying whether voting preferences in Alachua County are independent of gender. 83 voters from Alachua County were randomly sampled, and data was recorded on their gender and whether or not they voted for Romney or Obama in 2012. The results are summarized in the 2 & 2 contingency table below. Voted For Gender Obama Romney Total Female 29 15 44 Male 18 21 39 Total 47 36 83 (a) Verify that the assumptions for conducting a chi-squared test for independence have been met for this study. (b) State the hypotheses for this experiment. (c) Compute the test statistic X". (d) Find a range of values for the p-value and give the conclusion, using ̑ = 0.05. (e) We could also test H0 : p1 - p2 = 0 vs. Ha : p1 - p2 ≠ 0. Without explicitly conducting the significance test for comparing 2 independent proportions and using only the result in part (c), find the test statistic for comparing proportion of males who voted for Obama vs. proportion of females who voted for Obama. (f) Find the exact p-value for the significance test in part (e). What is the conclusion based on this p-value? (g) Does this conclusion of the significance test for comparing 2 independent proportions agree with the conclusion of the chi-square test for independence? Explain. (h) Compute the relative risk for proportion of women who voted for Obama to men who voted for Obama. What do we conclude? 4. Social scientists are often interested in social determinants for children's mental and physical well-being. In their study, Chase and Dummer interviewed students in grades 4-6 and asked them which goals were most important to them: grades, athletic ability, or popularity. In this problem, we will study the association (if any) between grade in school and goals.
Sri K.
Nuclear energy is a controversial topic in today's society. Many people have concerns about the safety and environmental impact of nuclear power. However, there are also those who argue that nuclear energy is a necessary and efficient source of electricity. In this essay, we will explore both sides of the debate and discuss the potential benefits and drawbacks of nuclear power. One of the main arguments in favor of nuclear energy is its ability to generate large amounts of electricity with relatively low carbon emissions. Unlike fossil fuels, which release greenhouse gases when burned, nuclear power plants produce electricity through a process called nuclear fission, which does not emit carbon dioxide. This makes nuclear energy a potentially attractive option for countries looking to reduce their carbon footprint and combat climate change. Another advantage of nuclear power is its high energy density. Nuclear fuel, such as uranium or plutonium, contains a tremendous amount of energy in a small volume. This means that a relatively small amount of nuclear fuel can produce a large amount of electricity, making nuclear power plants highly efficient. However, there are also significant concerns associated with nuclear energy. One of the most pressing issues is the problem of nuclear waste disposal. Nuclear power plants produce radioactive waste, which remains hazardous for thousands of years. Finding a safe and secure way to store this waste is a major challenge for the industry. Another concern is the potential for accidents or meltdowns at nuclear power plants. While modern reactors are designed with multiple layers of safety features, accidents can still occur. The most well-known example is the Chernobyl disaster in 1986, which resulted in a large release of radioactive material and significant environmental and health impacts. In conclusion, nuclear energy is a complex and controversial topic. While it offers the potential for clean and efficient electricity generation, there are also significant risks and challenges associated with its use. As the world continues to grapple with the need for sustainable and reliable energy sources, the debate over nuclear power will likely continue.
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