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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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- Shortleaf Pines. The ability to estimate the volume of a tree based on a simple measurement, such as the diameter of the tree, is important to the lumber industry, ecologists, and conservationists. Data on volume, in cubic feet, and diameter at breast height, in inches, for 70 shortleaf pines was reported in C. Bruce and F. X. Schumacher’s Forest Mensuration (New York: McGraw-Hill, 1935) and analyzed by A. C. Akinson in the article “Transforming Both Sides of a Tree” (The American Statistician, Vol. 48, pp. 307–312). The data are provided on the WeissStats site. a. obtain and interpret the standard error of the estimate. b. obtain a residual plot and a normal probability plot of the residuals. c. decide whether you can reasonably consider Assumptions 1–3 for regression inferences met by the two variables under consideration.The quality department at ElectroTech is examining which of two microscope brands (Brand A or Brand B) to purchase. They have hired someone to inspect six circuit boards using both microscopes. Below result in terms of a number of defects (e.g., solder voids, misaligned components) found using each microscope. (Note that the data for two brands can be paired) State all the assumptions required to define the test statistic. State the test Statistic in notations first and then calculate its value Find the p-value Carry out test of hypotheses at 1% level of significance and state the conclusion in context of problem. Calculate 99% confidence interval for the true average difference in defects found for two microscope brands.The Specific Absorption Rate (SAR) for a cell phone measures the amount of radio frequency (RF) energy absorbed by the user's body when using the handset. Every cell phone emits RF energy. Different phone models have different SAR measures. To receive certification from the Federal Communications Commission (FCC) for sale in the United States, the SAR level for a cell phone must be no more than 1.5 watts per kilogram. A sample of 47 models was tested and the average of their Specific Absorption Rates (SARs) was found to be 1.18 watts per kilogram. Assume that the population standard deviation is 0.25 watts per kilogram. Construct a 90% confidence interval for the mean of the SARs for cell phones that received certification from FCC. Margin of error (if applicable): (Round the answer to 2 decimal places)
- The Specific Absorption Rate (SAR) for a cell phone measures the amount of radio frequency (RF) energy absorbed by the user's body when using the handset. Every cell phone emits RF energy. Different phone models have different SAR measures. To receive certification from the Federal Communications Commission (FCC) for sale in the United States, the SAR level for a cell phone must be no more than 1.5 watts per kilogram. A sample of 47 models was tested and the average of their Specific Absorption Rates (SARs) was found to be 1.18 watts per kilogram. Assume that the population standard deviation is 0.25 watts per kilogram. Construct a 90% confidence interval for the mean of the SARs for cell phones that received certification from FCC. Confidence interval:( , ) Interpretation: We are % confident that the mean of the SARs for cell phones that received certification from FCC is between watts per kilogram and watts per kilogram.The Specific Absorption Rate (SAR) for a cell phone measures the amount of radio frequency (RF) energy absorbed by the user's body when using the handset. Every cell phone emits RF energy. Different phone models have different SAR measures. To receive certification from the Federal Communications Commission (FCC) for sale in the United States, the SAR level for a cell phone must be no more than 1.5 watts per kilogram. A sample of 47 models was tested and the average of their Specific Absorption Rates (SARs) was found to be 1.18 watts per kilogram. Assume that the population standard deviation is 0.25 watts per kilogram. Construct a 90% confidence interval for the mean of the SARs for cell phones that received certification from FCC. Point estimate: =watts per kilogram (Round the answer to 2 decimal places) Confidence level % and �= , also �2= , and 1-�2= Critical values: (Round the answer to 2 decimal places) left= right=A toolset from the Uniform Crime Reporting (UCR) Program by the FBI allows the public to view summarized crime data at a state level. The user accessing the website can select between viewing the violent crime rate or the property crime rate. Choose the best description of the type of data collected in this selection. A. Ranked categorical B. Binary categorical C. Discrete quantitative D. Continuous quantitative
- [Econometrics] The World Bank hires you to analyze the effect of the introduction of new irrigation systems in a series of Sub-Saharan African countries. They are particularly interested on their effect in the crop production of each country. They give you data for each country on the kilometers of irrigation tubes constructed, the total crop harvest, as well as information on the average educational attainment for each year between 2000 and 2017. Which type of analysis would you perform based on this information?No need to answer in detail Coronavirus is the most dangerous specially in adults where the mortality is high. In a case control study of this disease ,the children of adults were asked to fill in the questions in case the patient was deceased or could not fill in himself The controls were people who lived in the same area as the cases .only 64% of potential controls participated in thr study . Explain how this can create bias in the resultsHungry? Researchers investigated how the size of abowl affects how much ice cream people tend to scoopwhen serving themselves.14 At an “ice cream social,”people were randomly given either a 17 oz or a 34 ozbowl (both large enough that they would not be filledto capacity). They were then invited to scoop as muchice cream as they liked. Did the bowl size change theselected portion size? Here are the summaries: Test an appropriate hypothesis and state your conclu-sions. Assume any assumptions and conditions that you cannot test are sufficiently satisfied to proceed. Small Bowl Large Bowln 26 n 22y 5.07 oz y 6.58 ozs 1.84 oz s 2.91 oz
- Errors in medical prescriptions occur and a study1 examined whether electronic prescribing may help reduce errors. Two groups of doctors used written prescriptions and had similar error rates before the study. One group switched to e-prescriptions while the other continued to use written prescriptions, and error rates were measured one year later. The results are given in Table 1. Error No Error Total Electronic 254 3594 3848 Written 1478 2370 3848 Table 1 Are prescription error rates different? Find a 99% confidence interval for the difference in the two proportions, pw-pe, where pw is the proportion of errors using written prescriptions and pe is the proportion of errors using e-prescriptions.Round your answers to three decimal places.What type of data: The weight of cars crossing the Golden Gate Bridge. Qualitative Quantitative Discrete Quantitative ContinuousIncidence rate in the last influenza epidemic was found to be 50 per thousand (5%) of the population exposed. What should be the size of sample to find incidence rate in the current epidemic if allowable error is 0.005 and 0.01?