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Statistical Methods for Estimating Proportions and Confidence Intervals in Real-World Data Analysis

Description: The assignment delves into statistical methods used for data analysis, focusing on proportions and confidence intervals.

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    Statistical Methods for Estimating Proportions and Confidence Intervals in Real - World Data Analysis Quiz 6 1. A researcher wants to investigate the proportion of married men who are happy with their marriage t o do this, he takes a sample of 100 men and finds that 72 reported being happy with their marriage. Should a confidence interval be constructed to determine the proportion of all men who are happy with their marriage? Why? (give a short explanation; 1 - 2 sentences) Ans. Yes, a confidence interval should be constructed because it gives an interval around the point estimate of 72/100 ie 0.72 in which the researcher will find the population proportion of married men who are happy with their marriage with confidence(90 % or 95% or 99%). 2. Suppose a random sample of 64 cyclists on the Fred Meijer Heartland Trail was taken, of which 48 were wearing helmets. Find a 95% confidence interval for the proportion of all cyclists on the Fred Meijer Heartland Trail who wore helmets. Calculate the following quantities to lead you to the confidence interval. a. Standard Error: Sample Size(n) = 64 Point estimate p ̂ = 48/64 = 0.75 Standard Error = √( p ̂ * (1 - p ̂ )/n) = √(0.75 * 0.25 /64) = 0.0541 b. Margin of Error: Confidence Level (C.L.) = 0.95 α = 1 - C.L. = 1 - 0.95 = 0.05 z α/2 = 1.96 Margin of error = z * Standard error = 1.96 * 0.0541 = 0.1061 c. Critical Value: Confidence Level (C.L.) = 0.95 α = 1 - C.L. = 1 - 0.95 = 0.05 z α/2 = 1.96 = Critical Value d. Confidence Interval: Lower Limit = p ̂ - Margin of error = 0.75 – 0.1061 = 0.6439 Upper Limit= p ̂ + Margin of error = 0.75 + 0.1061 = 0.8561 3. A study was made investigating student enrollment persistence with respect to hours worked per week. Students classified as Preserving (those who returned after the first semester of college) and non - persevering (those who did not return after their first semester of college) were asked about the work schedules during the first semester of college. From these students, the following data was collected. Persevering Non - persevering (n=144) (n=49) # hrs worked per week in first semester Mean 17.4 28.64 SD 15.2 10.3

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