Sampling Distributions & Confidence Intervals for Proportions: Rules & Calculations - Prof, Study notes of Business Statistics

Download Sampling Distributions & Confidence Intervals for Proportions: Rules & Calculations - Prof and more Study notes Business Statistics in PDF only on Docsity! Jessica Wang Chapter 9: Sampling Distributions and Confidence Intervals for Proportions  Statistics: o x̄ , mean of sample o s, standard deviation of the sample o p̂ , sample proportion  Parameters: o µ, mean of population o σ, standard deviation of population o p, population proportion  Sampling distribution: distribution of the statistic obtained from repeated samples (or repeated trials of an experiment) using the same number of observations o Changes with parameter  Sample proportions: The proportion of “successes” can be more informative than the count. In statistical sampling the sample proportion of successes is used to estimate the proportion p of successes in a population. o For any SRS of size n, the sample proportion of successes is: p̂= count of successes in the sample n = X n o Rules for Sample Proportion:  A population with a fixed proportion p  Random Sample (independent, equal chance)  Sample size is large, np > 9 and n(1-p) > 9 o If the sample size is much smaller than the size of a population with proportion p of successes, then the mean and standard deviation of p̂ are: μ p̂=p  σ p̂=√ p(1−p )n o Because the mean is , we say that the sample proportion in an SRS is an unbiased estimator of the population proportion p o The variability decreases as the sample size increases. So larger samples usually give closer estimates of the population proportion p Confidence Interval of a Sample Proportion o Statement: Ex - We are 95% confident that between 24%-2*1.9% and 24%+2*1.9% of people in Washington agree with the recent changes to bankruptcy laws. < The proportion of the population o 95% confidence  95% of samples of this size will produce confidence intervals that capture the true proportion of the population (and we expect 5% of our samples to produce intervals that fail to capture the true proportion)