AMOUNT 48.16 AMOUNT 42.22 CONFIDENCE INTERVAL FOR μ, WHEN σ IS UNKNOWN 46.82 Mean 49.348 51.45 Standard Error 2.01517 TO APPLY THE FOLLOWING, YOU NEED TO HAVE DATA ANALYSIS (Excel) - The steps to up-load DATA ANALYSIS apear on BB under Course Content 23.78 Median 49.995 Steps: 41.86 Mode #N/A 1. Please enter the data in any column. You may include the title, in this case AMOUNT 54.86 Standard Deviation 9.01211 2. Click Data 37.92 Sample Variance 81.2182 3. Click Data Analysis 52.64 Kurtosis 2.25871 4. Choose Descriptive statistics 48.59 Skewness -0.99608 5. Put the range of the data in the Input Range. If the title of the data is included in the Input Range, in this case AMOUNT, select Labels in first row. 50.82 Range 38.05 6. Write the cell in the Output Range, where you want the ouput to appear 46.94 Minimum 23.78 7. Select Summary Statistics 61.83 Maximum 61.83 8. Select Confidence Interval for the mean (note: the default is 95%) and type in the confidence interval of interest 61.69 Sum 986.96 49.17 Count 20 61.46 Confidence Level(95.0%) 4.2178 Note that 4.217798 is the margin of error. To check: t(0.05, 19) 2.09302 NOTE: 0.05 is the area of both tails 51.35 The standard error is = 2.01517 which is = 2.01517 52.68 58.84 43.88 LOWER CONFIDENCE LIMIT 45.1302 Margin of error = 4.2178 which is the same as in D17. UPPER CONFIDENCE LIMIT 53.5658 Thus the 95% confidence interval is (45.132, 53.5658) If we are asked to interpret this: We can say we are 95% sure μ lies between 45.132 and 53.5658. A better interpretation is: If we select several samples and construct 95% confidence intervals like the above one, then we can say 95% of the intervals constructed contain μ. However, we do not know which ones do or do not contain μ. n s

CI for Pop Mean with unknown σ

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AMOUNT

48.16 AMOUNT

42.22 CONFIDENCE INTERVAL FOR μ, WHEN σ IS UNKNOWN

46.82 Mean 49.348

51.45 Standard Error 2.01517 TO APPLY THE FOLLOWING, YOU NEED TO HAVE DATA ANALYSIS (Excel) - The steps to up-load DATA ANALYSIS apear on BB under Course Content

23.78 Median 49.995 Steps:

41.86 Mode #N/A 1. Please enter the data in any column. You may include the title, in this case AMOUNT

54.86 Standard Deviation 9.01211 2. Click Data

37.92 Sample Variance 81.2182 3. Click Data Analysis

52.64 Kurtosis 2.25871 4. Choose Descriptive statistics

48.59 Skewness -0.99608 5. Put the range of the data in the Input Range. If the title of the data is included in the Input Range, in this case AMOUNT, select Labels in first row.

50.82 Range 38.05 6. Write the cell in the Output Range, where you want the ouput to appear

46.94 Minimum 23.78 7. Select Summary Statistics

61.83 Maximum 61.83 8. Select Confidence Interval for the mean (note: the default is 95%) and type in the confidence interval of interest

61.69 Sum 986.96

49.17 Count 20

61.46 Confidence Level(95.0%) 4.2178 Note that 4.217798 is the margin of error. To check: t(0.05, 19) 2.09302 NOTE: 0.05 is the area of both tails

51.35 The standard error is = 2.01517 which is = 2.01517

52.68

58.84

43.88 LOWER CONFIDENCE LIMIT 45.1302 Margin of error = 4.2178 which is the same as in D17.

UPPER CONFIDENCE LIMIT 53.5658

Thus the 95% confidence interval is (45.132, 53.5658)

If we are asked to interpret this: We can say we are 95% sure μ lies between 45.132 and 53.5658.

A better interpretation is: If we select several samples and construct 95% confidence intervals like the above one, then we can say 95% of the intervals constructed contain μ.

However, we do not know which ones do or do not contain μ.