STA 2023 Exam 2, Top Questions With Accurate Answers, rated A+. Verified.

STA 2023 Exam 2, Top Questions With Accurate Answers, rated A+. Verified. p̂ - -the sample proportion p̂= x/n (#successes/total # in sample) What are the assumptions of that must hold for the sampling distribution of the sample proportion to be normally distributed? - -np≥15 *AND* n(1-p)≥15 If our assumptions are met, what is the mean of the sampling distribution of the sample proportion? - -p (the population mean) T/F: The sample proportion and sample mean are random variables. - -True. How can you distinguish question about the sampling distribution of the sample proportion from a question about the sampling distribution of the sample mean? - -will often include the word "proportion," a percentage, and a deal with with categorical values If you know you are dealing with a sampling distribution question and you see that the standard deviation is given, what can you assume? - -You can assume that you are dealing with a question about the sampling distribution of the sample mean and *NOT* the sampling distribution of the sample proportion. Describe the sampling distribution of the sample proportion, assuming np≥15 and n(1-p)≥15. - -p̂~N(p, √(p(1-p)/n)) T/F: If np≤15 and n(1-p)≤15, you can add 2 successes and 2 failures to the approximate sampling distribution for the sample proportion. - -*FALSE.* This "trick" *ONLY* works with confidence intervals. If np≤15 and n(1-p)≤15, you cannot work with the sampling distribution of the sample proportion because you cannot assume that it is normal. x̄ - -The sample mean, which is the average of the observations in our sample. What are the assumptions that must hold true for the sampling distribution of the sample mean to be normally distributed? - -n≥30 or the original population was normally distributed If the sampling distribution of the sample mean is normally distributed, what is its mean? - -The population mean (μ) Describe the sampling distribution of the sample mean, assuming n≥30 or the original population was normally distributed. - -x̄~N(μ, σ/√n) Central Limit Theorem - -Even when the population's probability distribution is not bell shaped, the sampling distribution of the sample mean is bell-shaped when the same size is large enough (n≥30). Population Distribution - -The distribution for the overall population, which is based on parameters such as the population mean and the population standard deviation. Data Distribution - -The distribution of the data we collect in practice. We collect samples in order to create a data distribution so that we can estimate the population. The larger the sample size, the more the better the data distribution approximates the population distribution. The data distribution looks more like the population distribution when the sample size is (low/high). - -high Sample means tend to cluster more around the population mean when the sample size is (low/high). - -high A _____ is a numerical summary of the data in a population, and a _____ is a numerical summary of the data in a sample. - -parameter; statistic Point Estimates - -• Statistics that are used as "best guesses" for parameters • Sample mean point estimate for population mean • Sample stdev. estimate for population stdev. • Sample proportion point estimate for population proportion Interval Estimates - -Describe a range over which we can reasonably confident that the population parameter lies. Bias vs. Variability - -Biased: sampling distribution *not* centered at the parameter of interest Variability: sampling distribution has a large stderror and this highly spread out Inferential Statistics - -The branch of statistics that uses sample statistics to estimate population parameters. Confidence Interval - -Estimator ± Margin of Error Estimator - -x̄ (sample mean) to estimate μ (population mean) p̂ (sample prop) to estimate p (population prop) Confidence Interval for a Population Proportion - -p̂ ± z(√p̂(1-p̂)/n) Confidence Interval for a Population Mean - -x̄ ± t(s/√n) What is the margin of error in a confidence interval for a population proportion? - -z(√p̂(1-p̂)/n) What is the margin of error in a confidence interval for a population mean? - -t(s/√n) A sampling distribution is a probability distribution for a (parameter/statistic). - -statistic If our assumptions are met, what is the standard error of the sampling distribution of the sample proportion? - -stderror= √(p(1-p)/n) If the sampling distribution of the sample mean is normally distributed, what is its standard error? - -stderror= σ/√n