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Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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- In this study, the protection of aquatic ecosystems is an important goal of Ville de Montréal. In particular, Thomas wants to see whether the contamination of creeks (ruisseaux in French) by Escherichia coli differs among the months of May, June, July, and August. Therefore, herandomly samples six creeks in different areas. For each creek, he collects water samples from May to August, and measures the amount of E. coli, expressed in colony-forming units (CFU) per 100 mL of water. For each combination of a month and a creek, he thus obtains an E. coli contamination value, i.e., 24 observations in total. A preliminary statistical analysis produces the following results. Which pairs of months show significant differences in mean E. coli contamination? Explain your reasoning and justify your answer to this question with the results of a statistical procedure. Use α = 0.05.In this study, the protection of aquatic ecosystems is an important goal of Ville de Montréal. In particular, Thomas wants to see whether the contamination of creeks (ruisseaux in French) by Escherichia coli differs among the months of May, June, July, and August. Therefore, herandomly samples six creeks in different areas. For each creek, he collects water samples from May to August, and measures the amount of E. coli, expressed in colony-forming units (CFU) per 100 mL of water. For each combination of a month and a creek, he thus obtains an E. coli contamination value, i.e., 24 observations in total. A preliminary statistical analysis produces the following results. Which pairs of months show significant differences in mean E. coli contamination? Explain your reasoning and justify your answer to this question with the results of a statistical procedure. Use α = 0.05. Data: May= 66, June= 104, July=105, August= 88In this study, the protection of aquatic ecosystems is an important goal of Ville de Montréal. In particular, Thomas wants to see whether the contamination of creeks (ruisseaux in French) by Escherichia coli differs among the months of May, June, July, and August. Therefore, herandomly samples six creeks in different areas. For each creek, he collects water samples from May to August, and measures the amount of E. coli, expressed in colony-forming units (CFU) per 100 mL of water. For each combination of a month and a creek, he thus obtains an E. coli contamination value, i.e., 24 observations in total. A preliminary statistical analysis produces the following results. Part A: Does the mean E. coli contamination differ significantly among the four months? Justify your answer to this question with the result of a statistical test. Use α = 0.05. Part B:Which pairs of months show significant differences in mean E. coli contamination? Explain your reasoning and justify your answer to this…
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- In a certain jurisdiction, all students in Grade Three are required to take a standardized test to evaluate their math comprehension skills.The attached contains these data resulting from a random sample of n=40 schools within this jurisdiction. From these data you wish to estimate the model Yi=β0+β1Xi+ei where Xi is the percentage of Grade Three students in School i who live below the poverty line and Yi is the average mathematics comprehension score for all Grade Three students in the same school, School i. The observed data for the X variable is labled perbelowpoverty and the obvserved data for the Y variable is labeled mathscore in the .csv file.Import (either hand type or load the file) data into R Studio, then answer the following questions based on the data.(a) Create a scatterplot of the data. What can you say about the nature of the relationship between the percentage of Grade Three students living below the poverty line in a certain school and the school's average Grade Three…Doritos chips are one of the most popular chips in the year 2020. Frito-Lay produces snack-sized bags of Doritos with 1.75-ounce bags. Unfortunately, Frito-Lay has received many complaints that the bags of chips lack the promised amount of chips. PepsiCo, the owner of Frito-Lay, decide to run an internal investigation of their Doritos chip production. They sample around 500 bags of chips to discover that they found an average of 1.59 ounces with a standard deviation of .12 ounces. Conduct a hypothesis test with an alpha-level of .05. Should they change their production of Doritos chips to match the 1.75 ounces on the bag?Some shrubs have the useful ability to resprout from their roots after their tops are destroyed. Fire is a particular threat to shrubs in dry climates, as it can injure the roots as well as destroy the aboveground material. One study of resprouting took place in a dry area of Mexico. The investigation clipped the tops of samples of several species of shrubs. In some cases, they also applied a propane torch to the stumps to simulate a fire. Of 17 specimens of a particular species, 6 resprouted after fire. Estimate with 95% confidence the proportion of all shrubs of this species that will resprout after fire.Interval:
- #20 on psych stats show full workA study is run to evaluate the effectiveness of an exercise program in reducing systolic blood pressure in patients with pre-hypertension (defined as a systolic blood pressure between 120-139 mmHg or a diastolic blood pressure between 80-89 mmHg). A total of 7 patients with pre-hypertension enroll in the study, and their systolic blood pressures are measured. Each patient then participates in an exercise training program where they learn proper techniques and execution of a series of exercises. Patients are instructed to do the exercise program 3 times per week for 6 weeks. After 6 weeks, systolic blood pressures are again measured. The data are shown below. Is there is a difference in systolic blood pressures after participating in the exercise program as compared to before? State the hypotheses. What statistical test should be used to determine if there is a difference in systolic blood pressures before and after the exercise program? Determine the appropriate critical value and set…KJZZ, a local jazz station, has hired you as a research consultant to determine which demographic groups should be the radio station market. In particular, the station believes that there is a difference between men and women in terms of their opinions of jazz music. By randomly sampling men and women from the Houston metropolitan region, you calculate the results in Table 1. You also calculate a gamma of .064 and a chi-square of 1.99 with 2 degrees of freedom from the table. Note that the measure of association (gamma) of .064 indicates a very weak relationship between gender and like of jazz.In a paragraph of at least five to six sentences, discuss whether the percent distribution of the cross-tab, the measure of association, and chi-square supports, or does not support, the station’s hypothesis. Ensure that you mention hypothesis how the IV percent distribution changes in relationship to the DV what level of significance you used, and how the chi-square obtained from the sample…