8.2

• estimating a population mean: the basics 
• when we have only a single sample, the sample mean is the best extimate of the population mean,u 
• however, we do not expect the sample mean to be equal to the population mea, because there is likely to be some sampling error. Therfore, in order to make an inference about the population mean, we need some way 
• a precise calculation shows that if the distrubution of sample means is normal with a mean of u, then 95% of all sample means lie within 1.96 standard deviations of the population mean; for our purposes in this book, we will approximate this as 2 standard deviations 
• a confidence interval is a range of values likely to contain the true value of the population mean 
• the margin of error E= 2s/square root  of n 
• we find the 95% confidence interval by adding and subtracting the margin of error 
• interperting the confidence interval 
• a study
• E= 2s/ square root of n 
• square root of n = 2s/e 
• n = 2s/e ^2
• in order to estimate the population mean with a specified margin of error of at most E, the size of the sample should be at least 
• you want to study housing costs in the country by sampling recent house sales in various (representative) regions. Your goal is to provide a 95% confidence interval estimate of the housing cost. Previous studies suggest that the population standard deviation is about 7200. What sample size ( at a minimum) should be used to ensure the sample mean is within
• $500 of the true population mean
• $100 if the true population mean
• margin of error 
• based on a random sample of hospital costs for car crash victims, the sample mean is 9004 and the margin of error for a 95% confidence interval is $266 
• $8738<u$9270 
• the national health examination involves measurments from about 2500 people, and the results are used to estimate values of various poulations means. Is it valid to criticize this survey because the sample size is only about 0.01% of the population of all Americans? Explain 
• does it make sense 
• margin of error 
• the mean income of high school mathematics teachers estimated to be 48,213 
• finding margin of error and confidence intervals 
• sample size = 81 
• sample mean 4.5km 
• sample standard deviation 3.1 km  
• 0.7 km margin of error 
• 95% confidence interval for a population proportion 
• for a population proportion, the margin of error for the 95% confidence interval is 2 square root of p hat (1-p)/n
• p hat is the sample proportion 
• the neilsen ratings for television use a random sample of households. A nielsen survey results in an estimate that a women's world cup soccer game had 72.3% of the entire viewing audience. Assuming that the sample consists of n = 5000 randomly selected households, find the margin of error and the 95% confidence interval for this estimate 
• choosing the correct sanple size 
• in order to estimate a population proportion with a 95% degree of confidence and a specified margin of error of E, the size of the sample should be at least 
• n=1/E^2
• a study done by a reasearchers at Alfred University concluded that 80% of all student athletes in his country have been subjected to some form of hazing. 
• a study comiisioned by the U.S department of education