5. Using Excel - confidence intervals for the population mean (population standard deviation unknown) A rifle manufacturer is developing a new sniper rifle with an advanced automatic sighting mechanism. To test the accuracy of the sighting mechanism, five rifles are randomly selected. Each rifle is fired at the same target, and the vertical distance and horizontal distance between the shot and the target are measured (the error). (If the shot is to the left of the target, the horizontal distance is recorded with a minus sign; if the shot is below the target, the vertical distance is recorded with a minus sign.) Consider the horizontal error (in centimeters) to be a random variable x; assume that x follows a normal distribution with an unknown population mean, μ, and standard deviation, σ. The rifle manufacturer wants the population mean of x to be zero, because this suggests that the automatic sighting mechanism, on average, is accurate. To answer the questions that follow, download an Excel®® spreadsheet containing five observed values of the variable x by clicking on the following words in bold: Download Excel File Go through the following steps to compute a 90% confidence interval for the population mean of x. First, to produce an output similar to the table shown, use Excel 2010’s Descriptive Statistics tool by clicking the Data tab on the Ribbon. In the Data Analysis group, select Descriptive Statistics. Specify the input range of A1:A6, check Labels in first row, and specify the Output Range of B1. Finally, check the boxes for Summary statistics and Confidence Level for Mean. Enter the appropriate confidence level In the following sample Excel sheet, enter the value of the mean in cell C3 (rounded to five decimal places), and enter the margin of error in cell C16 (rounded to six decimal places). NOTE: Excel uses the label "Confidence Level (90%)" instead of margin of error. A B C 1 Horizontal Error, x 2 0.0028 3 0.0015 Mean _________ 4 –0.0052 Standard Error 0.001728699 5 0.0052 Median 0.0016 6 0.0016 Mode #N/A 7 Standard Deviation 0.003865488 8 Sample Variance 0.000014942 9 Kurtosis 2.777270793 10 Skewness –1.373334017 11 Range 0.0104 12 Minimum –0.0052 13 Maximum 0.0052 14 Sum 0.0059 15 Count 5 16 Confidence Level (90%) __________ You can be 90% confident that the population mean of x is between_______ and ________ .
5. Using Excel - confidence intervals for the population mean (population standard deviation unknown) A rifle manufacturer is developing a new sniper rifle with an advanced automatic sighting mechanism. To test the accuracy of the sighting mechanism, five rifles are randomly selected. Each rifle is fired at the same target, and the vertical distance and horizontal distance between the shot and the target are measured (the error). (If the shot is to the left of the target, the horizontal distance is recorded with a minus sign; if the shot is below the target, the vertical distance is recorded with a minus sign.) Consider the horizontal error (in centimeters) to be a random variable x; assume that x follows a normal distribution with an unknown population mean, μ, and standard deviation, σ. The rifle manufacturer wants the population mean of x to be zero, because this suggests that the automatic sighting mechanism, on average, is accurate. To answer the questions that follow, download an Excel®® spreadsheet containing five observed values of the variable x by clicking on the following words in bold: Download Excel File Go through the following steps to compute a 90% confidence interval for the population mean of x. First, to produce an output similar to the table shown, use Excel 2010’s Descriptive Statistics tool by clicking the Data tab on the Ribbon. In the Data Analysis group, select Descriptive Statistics. Specify the input range of A1:A6, check Labels in first row, and specify the Output Range of B1. Finally, check the boxes for Summary statistics and Confidence Level for Mean. Enter the appropriate confidence level In the following sample Excel sheet, enter the value of the mean in cell C3 (rounded to five decimal places), and enter the margin of error in cell C16 (rounded to six decimal places). NOTE: Excel uses the label "Confidence Level (90%)" instead of margin of error. A B C 1 Horizontal Error, x 2 0.0028 3 0.0015 Mean _________ 4 –0.0052 Standard Error 0.001728699 5 0.0052 Median 0.0016 6 0.0016 Mode #N/A 7 Standard Deviation 0.003865488 8 Sample Variance 0.000014942 9 Kurtosis 2.777270793 10 Skewness –1.373334017 11 Range 0.0104 12 Minimum –0.0052 13 Maximum 0.0052 14 Sum 0.0059 15 Count 5 16 Confidence Level (90%) __________ You can be 90% confident that the population mean of x is between_______ and ________ .
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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5. Using Excel - confidence intervals for the population mean (population standard deviation unknown)
A rifle manufacturer is developing a new sniper rifle with an advanced automatic sighting mechanism. To test the accuracy of the sighting mechanism, five rifles are randomly selected. Each rifle is fired at the same target, and the vertical distance and horizontal distance between the shot and the target are measured (the error). (If the shot is to the left of the target, the horizontal distance is recorded with a minus sign; if the shot is below the target, the vertical distance is recorded with a minus sign.)
Consider the horizontal error (in centimeters) to be a random variable x; assume that x follows a normal distribution with an unknown population mean, μ, and standard deviation, σ. The rifle manufacturer wants the population mean of x to be zero, because this suggests that the automatic sighting mechanism, on average, is accurate.
To answer the questions that follow, download an Excel®® spreadsheet containing five observed values of the variable x by clicking on the following words in bold: Download Excel File
Go through the following steps to compute a 90% confidence interval for the population mean of x.
First, to produce an output similar to the table shown, use Excel 2010’s Descriptive Statistics tool by clicking the Data tab on the Ribbon. In the Data Analysis group, select Descriptive Statistics. Specify the input range of A1:A6, check Labels in first row, and specify the Output Range of B1. Finally, check the boxes for Summary statistics and Confidence Level for Mean. Enter the appropriate confidence level
In the following sample Excel sheet, enter the value of the mean in cell C3 (rounded to five decimal places), and enter the margin of error in cell C16 (rounded to six decimal places). NOTE: Excel uses the label "Confidence Level (90%)" instead of margin of error.
|
A
|
B
|
C
|
---|---|---|---|
1 | Horizontal Error, x | ||
2 | 0.0028 | ||
3 | 0.0015 | Mean |
_________
|
4 | –0.0052 | Standard Error | 0.001728699 |
5 | 0.0052 | 0.0016 | |
6 | 0.0016 | #N/A | |
7 | Standard Deviation | 0.003865488 | |
8 | Sample Variance | 0.000014942 | |
9 | Kurtosis | 2.777270793 | |
10 | Skewness | –1.373334017 | |
11 | Range | 0.0104 | |
12 | Minimum | –0.0052 | |
13 | Maximum | 0.0052 | |
14 | Sum | 0.0059 | |
15 | Count | 5 | |
16 | Confidence Level (90%) |
__________
|
You can be 90% confident that the population mean of x is between_______ and ________ .
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