Consider a situation that you might want to study through a statistical lens. The situation would require you to study a small sample and make an inference to the population. For example, you might want to understand how likely children are to complete their homework when considering their individual characteristics or maybe you want to understand if children who eat broccoli are more likely to complete their homework than those who do not. Respond to the following in a minimum of 100 words without reference: How would you select a test that was appropriate to answer your question? How would you rule out tests that were not appropriate to answer your question?    Post 2 replies to classmates or your faculty member. Be constructive and professional. This is a response from another student that I need to reply to in a minimum of 100 words without reference:  "Consider a situation that you might want to study through a statistical lens. The situation would require you to research a small sample and make an inference to the population. For example, you might want to understand how likely children are to complete their homework when considering their characteristics. Maybe you want to understand if children who eat broccoli are more likely to complete their homework than those who do not. · How would you select a test that was appropriate to answer your question? · How would you rule out tests that were not appropriate to answer your question?  1 - is the proportion of kids who eat broccoli who finish their homework.  2 - is the proportion of kids who do not eat broccoli who finish their homework.   Null Hypothesis  H0: 1 = 2 The proportion of kids who eat broccoli who finish their homework is equal to the proportion of kids who do not eat broccoli who finish their homework. Alternative Hypothesis H1: 1 > 2 The proportion of kids who eat broccoli who finish their homework is greater than the proportion of kids who do not eat broccoli who finish their homework. Are children who eat broccoli more likely to complete their homework than children who do not eat broccoli. Outcome: Did you complete your homework? (yes or no)  Predictor: Do you eat broccoli? (yes or no) Two populations:  Kids who eat broccoli and kids who do not eat broccoli.   We need a test that can compare two proportions. Two proportion Z-test as long as we have enough data. We need a sample of about five kids in each group who report finishing or not finishing their homework.    We can rule out the test that needs a continuous outcome. (t-test, c, etc.) "

Hi, the RMarkdown and probability knowledge is needed. BUT I have answers as reference. All I need is some modification in case for the plagiarism. I need the answer to question 4 and 5 in Problem one. Due is Mar 8 at 3 pm. No extension. I have attached answers and questions and Thank you!

The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of 50 business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of 50 business travelers follow.378910101099998567798109876879539101099898610847310898101088Develop a 95% confidence interval estimate of the population mean rating for Miami. Round your answers to two decimal places. Enter your answer using parentheses and a comma, in the form (n1,n2). Do not use commas in your numerical answer (i.e. use 1200 instead of 1,200, etc.)Suppose a random sample of size 53 is selected from a population with σ = 9. Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate). a. The population size is infinite (to 2 decimals).b. The population size is N = 50,000 (to 2 decimals).c. The population size is N = 5000 (to 2 decimals).d. The population size is N = 500 (to 2 decimals).The budgeting process for a midwestern college resulted in expense forecasts for the coming year (in $ millions) of $9, $10, $11, $12, and $13. Because the actual expenses are unknown, the following respective probabilities are assigned: 0.28, 0.2, 0.2, 0.13, and 0.19. Show the probability distribution for the expense forecast. xf(x)910111213What is the expected value of the expense forecast for the coming year (to 2 decimals)? What is the variance of the expense forecast for the coming year (to 2 decimals)? If income projections for the year are estimated at $12 million, how much profit does the college expect to make (report your answer in millions of dollars, to 2 decimals)?A simple random sample of 700 individuals provides 100 Yes responses.a. What is the point estimate of the proportion of the population that would provide Yes responses (to 2 decimals)? b. What is your estimate of the standard error of the proportion (to 4 decimals)? c. Compute the 95% confidence interval for the population proportion (to 4 decimals).( , )America's young people are heavy Internet users; 87% of Americans ages 12 to 17 are Internet users (The Cincinnati Enquirer, February 7, 2006). MySpace was voted the most popular website by 9% in a sample survey of Internet users in this age group. Suppose 1,600 youths participated in the survey. What is the margin of error, and what is the interval estimate of the population proportion for which MySpace is the most popular website? Use a 95% confidence level and round your answers to 3 decimals. For interval estimate Enter your answer using parentheses and a comma, in the form (n1,n2). Do not use commas in your numerical answer (i.e. use 1200 instead of 1,200, etc.)Margin error =Interval estimate =A sociologist was hired by a large city hospital to investigate the relationship between the number of unauthorized days that employees are absent per year and the distance (miles) between home and work for the employees. A sample of 10 employees was chosen, and the following data were collected.Distance to WorkNumber of Days Absent1734476685102125141144181Which of the following scatter diagrams accurately represents these data?Scatter Diagram #1 Scatter Diagram #2 Scatter Diagram #3 - Select your answer -Scatter diagram #1Scatter diagram #2Scatter diagram #3Item 1Consider the following three scatter diagrams of the residuals against the independent variable. Which of the following accurately represents the data?Scatter Diagram #1 Scatter Diagram #2Scatter Diagram #3 - Select your answer -Scatter diagram #1Scatter diagram #2Scatter diagram #3Item 2 Develop the least squares estimated regression equation (to 3 decimals).Days Absent = + DistanceIs there a significant relationship between the two variables? Use = .05.Compute the value of the F test statistic (to 2 decimals). The p-value is - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 6 What is your conclusion?- Select your answer -Conclude that there is a significant relationship between days missed and distance from workDo not conclude that there is a significant relationship between days missed and distance from workItem 7 What is the value of r2 (to 3 decimals)? Note: report r2 between 0 and 1. Did the estimated regression equation provide a good fit?- Select your answer -Yes, it provided an exceptionally good fitYes, it provided a reasonably good fitNo, it did not provide an acceptable fitItem 9 Use the estimated regression equation developed in part (c) to develop a 95% confidence interval for the expected number of days absent for employees living 5 miles from the company (to 1 decimal).( , )When a new machine is functioning properly, only 7% of the items produced are defective. Assume that we will randomly select two parts produced on the machine and that we are interested in the number of defective parts found.a. Using the Figure 5.3, select a tree diagram that shows this problem as a two-trial experiment. Here D: defective; G: not defective.1. 2. 3. 4. Choose the Correct option from the above tree diagrams:Select1234Item 1b. How many experimental outcomes result in exactly one defect being found?c. Compute the probabilities associated with finding no defects, exactly one defect, and two defects (to 4 decimals).P (no defects)P (1 defect)P (2 defects)Consider the following hypothesis test:H0: μ ≤ 50Ha: μ > 50A sample of 60 is used and the population standard deviation is 6. Use the critical value approach to state your conclusion for each of the following sample results. Use α = .05. a. With x = 52.5, what is the value of the test statistic (to 2 decimals)? Can it be concluded that the population mean is greater than 50?- Select your answer -YesNoItem 2b. With x = 51, what is the value of the test statistic (to 2 decimals)? Can it be concluded that the population mean is greater than 50?- Select your answer -YesNoItem 4c. With x = 51.8, what is the value of the test statistic (to 2 decimals)? Can it be concluded that the population mean is greater than 50?- Select your answer -YesNoItem 6In San Francisco, 30% of workers take public transportation daily (USA Today, December 21, 2005). In a sample of 7 workers, what is the probability that exactly three workers take public transportation daily (to 4 decimals including interim calculations)? In a sample of 7 workers, what is the probability that at least three workers take public transportation daily (to 4 decimals including interim calculations)?The following data on price ($) and the overall score for 6 stereo headphones that were tested by Consumer Reports were as follows.BrandPriceScoreBose18077Scullcandy16072Koss9567Phillips/O'Neill7058Denon7040JVC3527a. Does the t test indicate a significant relationship between price and the overall score? The test t-Conclusion at α = .05t = (to 2 decimal places.)p-value is - Select your answer -less than .02between .02 and .05between .05 and .1between .1 and .2greater than .2Item 2What is your conclusion? Use α = .05.- Select your answer -There is a significant relationship between price and overall scoreThere is no significant relationship between price and overall scoreItem 3 .b. Test for a significant relationship using the F test. p-value is - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .1greater than .1Item 4What is your conclusion? Use α = .05.Because p-value is - Select your answer -greater than or equal toless than or equal toequal toItem 5 .05, we - Select your answer -acceptrejectItem 6 H0: β1 is - Select your answer -greater than or equal to zeroless than or equal to zeroequal to zeroItem 7 .c. Show the ANOVA table for these data. Round your answers to three decimal places, if necessary.Source of VariationSum of SquaresDegrees of FreedomMean SquareFp-valueRegression- Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .1greater than .1Item 12ErrorTotal40 mins ago