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 vertical 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 Vertical Error, x 2 –0.0014 3 0.0058 Mean _________ 4 0.0055 Standard Error 0.001372807 5 0.0038 Median 0.0038 6 0.0011 Mode #N/A 7 Standard Deviation 0.003069691 8 Sample Variance 0.000009423 9 Kurtosis –1.235544668 10 Skewness –0.712034776 11 Range 0.0072 12 Minimum –0.0014 13 Maximum 0.0058 14 Sum 0.0148 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 vertical 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 Vertical Error, x 2 –0.0014 3 0.0058 Mean ___ 4 0.0055 Standard Error 0.001372807 5 0.0038 Median 0.0038 6 0.0011 Mode #N/A 7 Standard Deviation 0.003069691 8 Sample Variance 0.000009423 9 Kurtosis –1.235544668 10 Skewness –0.712034776 11 Range 0.0072 12 Minimum –0.0014 13 Maximum 0.0058 14 Sum 0.0148 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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Author:Amos Gilat

Publisher:Amos Gilat

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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 vertical 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	Vertical Error, x
2	–0.0014
3	0.0058	Mean	_________
4	0.0055	Standard Error	0.001372807
5	0.0038	Median	0.0038
6	0.0011	Mode	#N/A
7		Standard Deviation	0.003069691
8		Sample Variance	0.000009423
9		Kurtosis	–1.235544668
10		Skewness	–0.712034776
11		Range	0.0072
12		Minimum	–0.0014
13		Maximum	0.0058
14		Sum	0.0148
15		Count	5
16		Confidence Level (90%)	_________

You can be 90% confident that the population mean of x is between_____ and ______ .

Definition Definition Measure of central tendency that is the value that occurs most frequently in a data set. A data set may have more than one mode if multiple categories repeat an equal number of times. For example, in a data set with five item—3, 5, 5, 29, 473—the mode is 5 because it occurs twice and no other value occurs more than once. On a histogram or bar chart, the element with the highest bar represents the mode. Therefore, the mode is sometimes considered the most popular option. The mode is useful for nominal or categorical data (e.g., the most common color car that users purchase), but it is problematic for continuous data because it is more likely not to have any value that is more frequent than the other.

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