Area Gas Prices - Random Sample Minneapolis Price of Regular Station Unleaded 1 $3.24 2 $3.03 3 $3.63 4 $3.58 5 $2.94 6 $3.68 7 $3.14 8 $3.36 9 $3.40 10 $3.20 11 $2.85 12 $3.80 13 $3.31 14 $3.78 15 $3.43 16 $3.27 17 $3.18 18 $3.48 19 $3.00 20 $3.36 21 $3.52 22 $3.26 23 $3.04 24 $3.17 25 $3.26 26 $3.27 27 $3.30 28 $3.51 29 $3.80 30 $3.05 31 $3.56 32 $3.53 33 $2.96 34 $3.57 35 $3.58 End of worksheet Station 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 St. Paul Price of Regular Unleaded $3.05 $2.89 $3.84 $3.50 $2.78 $3.51 $3.33 $3.31 $3.20 $3.15 $2.75 $3.79 $3.10 $3.92 $3.31 $3.45 $3.17 $3.44 $2.93 $3.21 $3.37 $3.08 $3.04 $3.24 $3.17 $3.36 $3.25 $3.62 $3.88 $3.02 $3.68 $3.29 $2.81 $3.43 $3.44 Confidence Interval Calculator Confidence Interval for a Population Mean, Sigma Known If the population standard deviation is known, we can directly calculate the standard deviation of the sampling distribution (the standard error of the estimate) and use the standardized normal distribution to get a z-multiple, using the Excel function NORMSINV. The margin of error is the z-multiple times the standard error, and it is how far the confidence interval extends on each side of the point estimate. Input Variables: Sample mean (x-bar): 100 Population standard deviation (sigma): 15 Sample size (n): 50 Confidence level: 0.9 < Input the appropriate number for your situation. < Input the appropriate number for your situation. < Input the appropriate number for your situation. < Input the appropriate number for your situation. Intermediate Calculations: Standard error of the estimate: 2.1213203 Prob. in one-tail for this conf level: 0.05 Prob. to use in NORMSINV: 0.95 Z-multiple: 1.645 Confidence Interval: Lower limit: 96.51 Upper limit: 103.49 Margin of error: 3.49 We can be 90% confident that the population mean lies between 96.51 and 103.49 r for your situation. r for your situation. r for your situation. r for your situation. ent that the population mean d 103.49 Confidence Interval Calculator Confidence Interval for a Population Mean, Sigma Unknown If the population standard deviation is not known, we must use the sample standard deviation as an estimate and use it to calculate the standard deviation of the sampling distribution (the standard error of the estimate). We also use the t distribution to get a multiple corresponding to the desired confidence level, using the Excel function TINV. The margin of error is the t multiple times the standard error, and it is how far the confidence interval extends on each side of the point estimate. Input Variables: Sample mean (x-bar): 1000 Sample standard deviation (s): 500 Sample size (n): 70 Confidence level: 0.95 <-- Input the appropriate number for your situation. <-- Input the appropriate number for your situation. <-- Input the appropriate number for your situation. <-- Input the appropriate number for your situation. Intermediate Calculations: Degrees of freedom: 69 Standard error of the estimate: 59.76 Prob. in the tails for this conf level: 0.05 T-multiple: 1.995 Confidence Interval: Lower limit: 880.78 Upper limit: 1119.22 Margin of error: 119.22 We can be 95% confident that the population mean lies between 880.78 and 1119.22 population mean Confidence Interval Calculator Confidence Interval for a Population Proportion From a sample proportion we can calculate the standard deviation of the sampling distribution (the standard error of the estimate), and use the standardized normal distribution to get a z-multiple, using the Excel function NORMSINV. The margin of error is the z-multiple times the standard error, and it is how far the confidence interval extends on each side of the point estimate. Input Variables: Sample proportion (p-bar): 0.43 Sample size (n): 100 Confidence level: 0.95 <-- Input the appropriate number for your situation. <-- Input the appropriate number for your situation. <-- Input the appropriate number for your situation. Intermediate Calculations: Standard error of the estimate: 0.0495 Prob. in one-tail for this conf level: 0.025 Prob. to use in NORMSINV: 0.975 Z-multiple: 1.960 Confidence Interval: Lower limit: 0.3330 Upper limit: 0.5270 Margin of error: 0.0970 We can be 95% confident that the population proportion lies between 0.333 and 0.527 for your situation. for your situation. for your situation. ent that the population proportion Running head: ESTIMATING FROM SAMPLES Estimating From Samples Michelle Mc Donald- Upshaw MBA-FP6018 December 5, 2016 Professor: Jeffrey Edwards 1 ESTIMATING FROM SAMPLES 2 Estimating From Samples To: Star Tribune Manager, Practical Application Scenario 1 As the new manager of the data verification unit at the Star Tribune, I have been tasked to produce a ninety-five percent confidence interval for the average price of regular unleaded gasoline in the Minneapolis and Saint Paul, Minnesota area. A survey that includes random samples of regular unleaded gas from seventy of the area gas stations was conducted. The following information will shed light on the results of the practical application survey. Area Gas Prices - Random Sample Statio n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Minneapoli s Price of Regular Unleaded $3.24 $3.03 $3.63 $3.58 $2.94 $3.68 $3.14 $3.36 $3.40 $3.20 $2.85 $3.80 $3.31 $3.78 $3.43 $3.27 $3.18 $3.48 $3.00 $3.36 $3.52 $3.26 $3.04 Statio n 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 St. Paul Price of Regular Unleaded $3.05 $2.89 $3.84 $3.50 $2.78 $3.51 $3.33 $3.31 $3.20 $3.15 $2.75 $3.79 $3.10 $3.92 $3.31 $3.45 $3.17 $3.44 $2.93 $3.21 $3.37 $3.08 $3.04 ESTIMATING FROM SAMPLES 24 25 26 27 28 29 30 31 32 33 34 35 $3.17 $3.26 $3.27 $3.30 $3.51 $3.80 $3.05 $3.56 $3.53 $2.96 $3.57 $3.58 59 60 61 62 63 64 65 66 67 68 69 70 3 $3.24 $3.17 $3.36 $3.25 $3.62 $3.88 $3.02 $3.68 $3.29 $2.81 $3.43 $3.44 Input Variables: The known input variables provide the following summary: Sample means (x-bar): Sample standard deviation (s): Sample size (n): Confidence level: Confidence Interval: Lower limit: Upper limit: Margin of error: $3.32 0.28 70 0.95 $3.25 $3.39 0.07 Findings: The results show that ninety-five percent of the populations mean lies between a price of $3.25 and $3.39. There is also a marginal error of 7%. Finally, 5 out of 100 shops sell unleaded gas above $3.39 or below $3.25. Respectively Submitted, Michelle Mc Donald- Upshaw To: Microsoft Business Manager, ESTIMATING FROM SAMPLES 4 Practical Application Scenario 2 As the newest member of this elite Microsoft team, I have been assigned to investigate the proposal for replacing the existing coffee brewing units with German-made brewers. I am approaching this by developing a ninety-nine percent confidence interval for the yield of cups per pound for the new brewer. With the assumption that the margin of error is less than threetenths of a cup and the current coffee makers standard deviation of 1.2 cups, I have appropriately determined the sample to conduct my proposal to you. The known input variables are as follows: Inputs: Planning value for sigma: Desired Margin: Confidence Level: 1.2 0.3 0.99 Intermediate Calculations: Z - Multiple: 2.5758 Sigma Squared 1.44 M.E. Squared 0.09 Z-Multiple Squared 6.634897 Results: Sample size rounded to a whole number: 107 These results show that to adequately survey the proposal 107 cups of coffee per pound of the German coffee brewer is required. The confidence intervals are just point estimates. With the given confidence interval and the desired margin, 107 cups are the sample size needed based ESTIMATING FROM SAMPLES 5 on the confidence interval of ninety-nine percent. There is also a margin of error that will be three- tenths of a cup. Respectively Submitted, Michelle Mc Donald-Upshaw Conclusion In the first scenario, there was a conclusion made that ninety-five percent of the population means lie between $3.25 and $3.39 with an error of margin that is seven percent. Scenario two proved that 107 cups was needed based on a ninety-nine percent interval and a marginal error of three tenths of a cup of coffee