Inferential Statistics in Grade 11 SHS Dept

Stats11

1. INFERENTIAL STATISTICS

2. INFERENTIAL STATISTICS Branch of Statistics that pertains to the process of drawing and making decisions concerning a given population based on the data obtained from the sample.

3. INFERENTIAL STATISTICS ESTIMATION LINEAR REGRESSION HYPOTHESIS TESTING

4. TYPES OF ESTIMATION ESTIMATION A process for which a proposed value is obtained using the information gathered from a particular sample. Point Estimates - a single value/values that best determines the proposed parameter value of the population. ex. light bulbs last for 5 months Interval Estimates - range of values within which the parameter value possibly falls. ex. light bulbs last for 4-6 months.

5. INTERVAL ESTIMATE The middle 99% is the proportion of the regions above z = -2.58 and below z = 2.58 also called a confidence interval the interval of values that predicts where the true population parameter belongs CONFIDENCE INTERVAL the degree of certainty that the true population parameter falls within the constructed confidence interval. If your interval estimate is made using the 80% confidence level, it indicates that your estimate is correct 80% of the time. The middle 95% is the proportion of the regions above z = -1.96 and below z = 1.96 The middle 90% is the proportion of the regions above z = -1.65 and below z = 1.65

6. The middle 99% is the proportion of the regions above z = -2.58 and below z = 2.58 INTERVAL ESTIMATE

7. The middle 95% is the proportion of the regions above z = -1.96 and below z = 1.96 INTERVAL ESTIMATE

8. The middle 90% is the proportion of the regions above z = -1.65 and below z = 1.65 INTERVAL ESTIMATE

9. ESTIMATING POPULATION MEAN

10. Case 1: Estimating the Population Mean given the Population Standard Deviation   INTERVAL ESTIMATION

11. Case 2: Estimating the Population Mean using the Central Limit Theorem (Large Sample) INTERVAL ESTIMATION  

12. Case 3: Estimating the Population Mean using the T-distribution (Small Sample) INTERVAL ESTIMATION  

13. Problem Solving 1 The mean scores of a random sample of 47 students who took a special test is 83.5 with a standard deviation of 4.1. The sample comes from an approximately normal population, find the point and the interval estimates of the population mean adopting a confidence level of 95%.

14. Problem Solving 2 The average weight of 25 chocolate bars selected from a normally distributed population is 200 g. The population standard deviation is 10 g. Find the interval estimates using a 90% confidence level.