Scores on the math SAT are normally distributed. A sample of 20 SAT scores had standard deviation s = 87. Construct a 98% confidence interval for the population standard deviation \(\sigma\).
Equation transcription:
Text transcription:
\sigma
Elements of Statistics – Chapter 7 Notes Sampling Error An error that occurs when we use sampes to estimate a population characteristic The DIFFERENCE between the POPULATION NUMERICAL INFORMATION and the SAMPLE NUMERICAL INFORMATION Sampling Distribution Choosing a sample from the original population Sample Illustrative Example EX.1) You have a population of 4 people who gave the number of meals they ate per day : 1, 3, 5, 7 SUBJECTS A B C D # OF 1 3 5 7 MEALS PER DAY SAMPLE DISTRIBUTION with a sample size of 2 A + B 1 + 3 A + C 1 + 5 A + D 1 + 7 List of all B + C 3 + 5 Possible B + D 3 + 7 Samples C + D 5 + 7 Sampling Distribution of Sample Mean X = / (n) = Standard Deviation n = Sample Size X = Sample Mean X = = Population Mean Z = X - X / X Z = Z-Score Central Limit Theorem (CLT) If a smaple size is large enough the sampling distribution is normal with a symmetric curve If sample size is unknown, it is considered to be at least 30 EX.1) A tanning salon calculated the average ti