University:
University of Houston
Course:
MATH 1313 | Linear Algebra
Academic year:

2022
Views:

217

Pages:

11
Author:

Braelyn Harmon

Confidence Interval from a Proportion Inference #2: for large populations, this can be assumed to be true. Sample Statistics Critical Value: percent of confidence The formula for confidence intervals of proportions: This is taken from the Formula Sheet for Test 3, already posted on the casa calendar! R Studio / Calculator Assistance! For a confidence level of 95%, you are interested in the middle 95% of a standard deviation: 0.5 + 0.95/2 Essentially, you will always use: qnorm(1.##/2) ½ + 0.95/2 or InvNorm(1.##/2) 1.95/2 Example: n = 40, x = 25, CL: 90% Part a: p^ = x/n = 25/40 = 0.625 [0.499, 0.751] We are 90% certain that the proportion of Lenny’s free‐throw success for the season will be between 49.9% and 75.1% Note: If a preliminary proportion (p) is not given in the problem, use p = 0.50 Changes in the Confidence Interval: The following changes will result in an increase in the width of the confidence interval: Increase of Margin of Error Increase of Confidence Level Change in sample proportion nearer to 𝑝̂ 0.50 Decrease of Sample Size Popper 23: A simple random sample, of size 150, is selected from a large population. It is determined that, within this sample, 85% of people own their own vehicles. 1. Are the number of successes and failures appropriate for this method? a. Yes b. No 2. Determine the standard deviation or standard error for the sample selected. a. 0.0008 b. 0.069 c. 0.029 d. 0.85 3. Determine the margin of error with a confidence level of 90%. a. 0.90 b. 0.4365 c. 1.2823 d. 0.04796 4. Determine the confidence interval for this statistic. a. [.37, .85] b. [.802, .898] c. [.85, .90] d. [65, 235] 5. If the sample size were increased, what is a possible confidence interval: a. [.808, .892] b. [.802, .892] c. [.791, .909] d. [.808, .903] Decrease width of interval: increase low value, decrease high value by the same amount Popper 23: For a certain population, it is known that 85% of people own their own vehicles. A simple random sample, of size 150, is selected from this population. 6. Interpret the confidence interval. a. There is a 90% probability that the population proportion will be within the confidence interval b. There is a 90% probability that the mean of the sample will be 0.85. c. 90% of the 150 subjects own a vehicle. d. 85% of the 150 subjects fall within the confidence interval.