Confidence Intervals - Lab 6 | Statistical Methods | STAT 303, Lab Reports of Data Analysis & Statistical Methods

Download Confidence Intervals - Lab 6 | Statistical Methods | STAT 303 and more Lab Reports Data Analysis & Statistical Methods in PDF only on Docsity! Lab 6: Confidence Intervals Open Excel where we will generate normal data. 1. Go to ToolsData AnalysisRandom Number Generator. Type 20 for Number of Variables, 25 for Number of Random Numbers, Normal for Distribution, 30 for Mean, 5 for Standard Deviation, some ‘random’ four digits number for Random Seed (please be sure to remember this number or save the data you are creating because we will be using it again),  Output Range and click on the  and click in the A1 cell, click the  again and click Ok. You have now create 20 random normals that are N(30, 52). 2. Insert a blank line as the first line and label the columns x1 through x20. 3. At the bottom of the first column (line 27), type =AVERAGE(A2:A26) and hit Enter. Beneath this type =STDEV(A2:A26) and hit Enter. Copy and paste these commands under the other 19 columns. 4. While these two rows are still hilighted, right click Copy, move to cell U2 (the 2nd row in the first empty column), right click Paste Special,  Values,  Transpose. Label the first new column means and the 2nd sds. What value is the 1st column estimating? What value is the 2nd column estimating? 5. Now we want to compute confidence intervals for each trial, but first label the next columns: lower 90%, upper 90%, flag 90, lower 95%, upper 95%, flag 95, lower 99%, upper 99%, flag 99. To create the upper and lower bounds, we need the formula for confidence intervals: / 2x z n    . The mean is the column labelled means, the z/2 is the z-score for the 90 (or 95 or 99)% confidence interval,  is 5 (the number we gave in step 1), and n is 25 since we used 25 observations in each trial. The excel code for the lower bound of a 90% CI is = U2  1.645*5/sqrt(25). where U2 is the mean. You can then copy and paste the rest of the column. Continue for the other “upper” and “lower” columns using the correct z-score and + or  appropriately. What is happening as the confidence level increases? 6. After filling in the “upper” and “lower” columns, you now need to figure out which intervals DON’T contain the true mean,  = 30. If the lower is greater than 30, then the entire interval is above 30. If the upper bound is less than 30, then the entire interval is below 30. Either is a ‘miss’. Put an * in the flag column next to the interval that ‘misses’. How many 90% intervals SHOULD contain 30? 95%? 99%? How many of yours contain 30 for each of the 3 levels? Explain what the confidence level for a confidence interval means. Now we want to test the claim that the true mean is 30, H0:  = 30 vs. HA:   30. 7. First add labels for the next columns: test stat, p-value, < 0.10, < 0.05, < 0.01. These will be the test statistic, the p-value for the test statistic, and whether the p-value is less than  = 10%, 5% or 1%. 8. In the test stat column 2nd row, type =(U230)/(5/sqrt(25)) where U2 is the first mean. Copy this down the column for the other 19 test statistics. 9. To create the p-values, type =(1-NORMSDIST(ABS(AF2)))*2 where AF2 is the test statistic. This is finding 2*P(Z>|ts|), the p-value for a two-sided () test. 10. In the next 3 columns, put an * in the cell if the p-value is less than , the significance level. These are the tests that commited Type I errors. Why? How many flags do you expect to get in the <10% column? the <5%? the <1%? What is the relationship between making a Type I error and the confidence interval missing ? How can we use confidence intervals to carry out a hypothesis test?