# Project 4 Group 1

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Julia Bala Eleanor Vogelsang Grace Hughes PROJECT 4 Estimation of the Population Mean of Soft Plaque Deposit (Confidence Interval of the Mean). Estimation of the Population Proportion of Soft Plaque Deposit (Confidence Interval of the Proportion). This project uses the sample data of the experiment Atassi (A-1), shown here. Assume the variable, soft plaque deposit index, is approximately normally distributed. In a study of the oral home care practice and reasons for seeking dental care among individuals on renal dialysis, Atassi (A-1) studied 90 subjects on renal dialysis. The oral hygiene status of all subjects was examined using a plaque index with a range of 0 to 3 (0=no soft plaque deposits, 3=an abundance of soft plaque deposits). The following table shows the plaque index scores for all 90 subjects. 1.17; 2.50; 2.00; 2.33; 1.67; 1.33; 1.17; 2.17; 2.17; 1.33; 2.17; 2.00; 2.17; 1.17; 2.50; 2.00; 1.50; 1.50; 1.00; 2.17; 2.17; 1.67; 2.00; 2.00; 1.33; 2.17; 2.83; 1.50; 2.50; 2.33; 0.33; 2.17; 1.83; 2.00; 2.17; 2.00; 1.00; 2.17; 2.17; 1.33; 2.17; 2.50; 0.83; 1.17; 2.17; 2.50; 2.00; 2.50; 0.50; 1.50; 2.00; 2.00; 2.00; 2.00; 1.17; 1.33; 1.67; 2.17; 1.50; 2.00; 1.67; 0.33; 1.50; 2.17; 2.33; 2.33; 1.17; 0.00; 1.50; 2.33; 1.83; 2.67; 0.83; 1.17; 1.50; 2.17; 2.67; 1.50; 2.00; 2.17; 1.33; 2.00; 2.33; 2.00; 2.17; 2.17; 2.00; 2.17; 2.00; 2.17; This project has two parts. Part I. Confidence Interval on the Mean. Show the sample data. Describe the purpose for computing a confidence interval for the mean. (What you are setting out to find) Pick a confidence level of your choice. 1. Compute a sample mean. 163.55 90 = 1.8172 2. Describe the variable. The variable used is the mean soft plaque deposited index or the average of sample soft plaque deposite index which uses the 1-3 value. 0 being no soft plaque deposite and 3 being an abundance of soft plaque depostie. 3. Describe the confidence level you are taking and its specific meaning.
Chosen confidence level: α = 0.05 95% confidence level, meaning 95% of the time estimates of the interval of sample mean will include the population mean. 4. Show the confidence interval formula that you are using. μ±z s 2 n μ = mean s = sample SD n = sample ¿¿ z = valuedetermined by condifencelevel found ¿ z distributiontable 5. Show the reliability coefficient (critical value). Critical value= 1.96 for 95% confidence interval obtained from z distribution table 6. Show all the pertinent computations using the equation editor. confidenceinterval = 1.8172 ± 1.96 0.562548 2 90 =( 1.7010,1.9335 ) 7. Draw a conclusion in the context of the experiment. The average of oral hygiene status of all subjects lies between 1.7010 1.9335 at a 95% chance. Part II. Confidence Interval on the Proportion. Show the sample data. Describe the purpose for computing a confidence interval on the Proportion (What you are setting out to obtain) Pick a confidence level of your choice. 1.17; 2.50; 2.00; 2.33; 1.67; 1.33; 1.17; 2.17; 2.17; 1.33; 2.17; 2.00; 2.17; 1.17; 2.50; 2.00; 1.50; 1.50; 1.00; 2.17; 2.17; 1.67; 2.00; 2.00; 1.33; 2.17; 2.83; 1.50; 2.50; 2.33; 0.33; 2.17; 1.83; 2.00; 2.17; 2.00; 1.00; 2.17; 2.17; 1.33; 2.17; 2.50; 0.83; 1.17; 2.17; 2.50; 2.00; 2.50; 0.50; 1.50; 2.00; 2.00; 2.00; 2.00; 1.17; 1.33; 1.67; 2.17; 1.50; 2.00; 1.67; 0.33; 1.50; 2.17; 2.33; 2.33; 1.17; 0.00; 1.50; 2.33; 1.83; 2.67; 0.83; 1.17; 1.50; 2.17; 2.67; 1.50; 2.00; 2.17; 1.33; 2.00; 2.33; 2.00; 2.17; 2.17; 2.00; 2.17; 2.00; 2.17; 1. Compute a sample proportion of your choice (pick a certain index, count how many times it comes up in the sample, divide this frequency by sample size). Certain index= 2.00, Frequency= 18, Sample size= 90
p = 18 90 = 0.20 2. Describe the variable. The variable used is the proportion of soft plaque deposit index which is also the proportion sample of the soft plaque deposit index. 3. Describe the confidence level you are taking and its specific meaning. Chosen confidence level: α = .90 The confidence coefficient (same to confidence level) of 0.90 means there's a 90% confidence level therefore indicating that there is a 10% chance of being wrong. Meaning that there is a 90% chance of the time estimates of the interval of sample proportion will include the population mean. 4. Show the confidence interval formula that you are using. (p.s. couldn't get the p^ to insert correctly so below is what I got) 1 p ^ ¿ ¿ phat ¿ ¿ Confidence Interval = p ^ ± z ¿ 5. Show the reliability coefficient (critical value). Critical value= 1.65 for 90% confidence interval. 6. Show all the pertinent computations using the equation editor. ConfidenceInterval = 0.2 ± 1.65 0.2 ( 1 0.2 ) 90 = (0.1304 ,0.2696) 7. Draw a conclusion in the context of the experiment. The average proportion of soft plaque deposit index lies between 0.1304 and 0.2696 at a 90% chance. A grade level A implies: a . your project presents in full all the requirements of part I & part II; Attach the text and data of the research. You must provide your answers with all the applicable computations, formatted as word.doc using equation editor. You must answer the question(s) raised by this research. Each answer must be complete and correct . b. you submit your project on time;
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