interval estima null hypothesis and .pptx

Interval

1. UNDERSTANDING CONFIDENCE INTERVAL ESTIMATES FOR THE POPULATION MEAN WHEN KNOWN  

2. An interval estimate called a confidence interval is a range of values that is used to estimate a parameter. This estimate may or may not contain the true parameter value.

3. Confidence Level refers to the percentage of all possible samples that can be expected to include the true population parameter . Confidence Level Critical Value 80% ±1.28 90% ±1.65 95% ±1.96 98% ±2.33 99% ±2.58

4. How to compute the confidence interval estimates?

5. Confidence Level Critical Value 80% ±1.28 90% ±1.65 95% ±1.96 98% ±2.33 99% ±2.58 Determine the critical value of the given confidence level. S T E P S

6. E = z ( )   Positive Critical Value b) Find the maximum error/margin of error . Margin of Error (E) is an interval estimate — a pair of percentages surrounding a guess about some attribute of the full population based on a random sample from the population.

7. = X - E Lower Limit = X + E Upper Limit c) Find the lower and upper limits . Lower and Upper Limit  are the maximum or minimum values above or below which you are confident (at a selected confidence level) that the statistic will occur.

8. X – E < < X +E   d) Describe/interpret the results. Lower limit Upper limit

9. Example 1: The operations manager of a large production plant would like to estimate the mean amount of time a worker takes to assemble a new electronic component. Assume that the standard deviation of this assembly time is 3.6 minutes. After observing 121 workers assembling similar devices, the manager noticed that their average time was 16.2 minutes. Compute a 90% confidence interval for the mean assembly time.

10. Example 2: Given: X = 10.5 n = 49 Compute the confidence interval estimates using a 95% confidence level.  

11. 55 44 40 44 43 42 44 43 42 44 43 44 43 42 44 43 42 44 43 56 44 42 44 43 56 56 43 56 56 45 34 43 56 56 45 54 65 45 54 46 56 65 45 54 46 54 56 46 54 56 54 56 46 54 56 53 44 56 53 46 54 44 56 53 46 52 53 46 52 64 53 53 46 52 64 56 53 46 52 55 52 55 64 56 45 47 52 64 56 43 56 45 65 56 45 46 56 45 47 45 Find the point estimate . ACTIVITY 1:

12. ACTIVITY(1/2CW): Compute the confidence interval estimate of the population mean below. 1 .Suppose a simple random sample of 100 students is drawn from a population of college students. Among sampled students, the average IQ score is 115 with a standard deviation of 10. Compute the 99% confidence interval for the students' IQ score. 2. A particular store wants to estimate the average value of an item that it has in its inventory.   A random sample of 250 cards indicates an average value of P80 and a standard deviation of P5. Find the interval estimate adopting 98% confidence level.