Excel Project Excel and many other technologies are capable of generating normally distrib- uted data drawn...

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Excel Project Excel and many other technologies are capable of generating normally distrib- uted data drawn from a population with a specified mean and standard devia- tion. Bone density test scores are measured as z scores having a normal distri- bution with a mean of 0 and a standard deviation of 1. Generate two sets of sample data that represent simulated bone density scores, as shown below. TREATMENT GROUP: Generate 10 sample values from a normally dis- tributed population of bone density scores with mean 0 and standard devi- ation 1. PLACEBO GROUP: Generate 15 sample values from a normally distrib- uted population of bone density scores with mean 0 and standard devia- tion 1. To generate sample data in Excel follow these steps: 1. Click the Data tab in the Ribbon. 2. Click the Data Analysis button in the Ribbon. (If Data Analysis is not available, the Analysis ToolPak must be installed as described in Section 1-40). 3. The Data Analysis dialog box now appears. 4. Select Random Number Generation, and then click OK. 5. The Random Number Generation dialog box now appears as shown. a. Select Normal in the Distribution box. b. Enter a value for the Number of Variables (or the number of col- umns of data), Number of Random Numbers, Mean, and Standard Deviation. c. Click OK to generate the values. Random Number Generation ? Number of Variables: 1 OK Number of Random Numbers: 10 Cancel Distribution: Normal Parameters Mean = 0 Standard deviation = 1 Random Seed: Output options Output Range: New Worksheet Ply: New Workbook 9.4-59 Full Alternative Text Help 9.4-59 Full Alternative Text Because each of the two samples consists of random selections from a normally distributed population with a mean of 0 and a standard deviation of 1, the data are generated so that both data sets really come from the same population, so there should be no difference between the two sample means. a. After generating the two data sets, use a 0.10 significance level to test the claim that the two samples come from populations with the same mean. b. If this experiment is repeated many times, what is the expected per- centage of trials leading to the conclusion that the two population means are different? How does this relate to a type I error? c. If your generated data leads to the conclusion that the two population means are different, would this conclusion be correct or incorrect in reality? How do you know? d. If part (a) is repeated 20 times, what is the probability that none of the hypothesis tests leads to rejection of the null hypothesis? e. Repeat part (a) 20 times. How often was the null hypothesis of equal means rejected? Is this the result you expected? Long description Random Number Generation ? Number of Variables: 1 OK Number of Random Numbers: 10 Cancel Distribution: Normal Help Parameters Mean = Standard deviation = Random Seed: Output options 0 = 1 Back Qutput Range: New Worksheet Ply: New Workbook The window displays the following entries. The number of variables, 1. The number of ran- dom numbers, 10. Distribution, normal. Parameters. Mean, 0. Standard deviation, 1. From the radio button under the heading Output options, New worksheet Ply is selected. Back Excel Project Excel and many other technologies are capable of generating normally distrib- uted data drawn from a population with a specified mean and standard devia- tion. Bone density test scores are measured as z scores having a normal distri- bution with a mean of 0 and a standard deviation of 1. Generate two sets of sample data that represent simulated bone density scores, as shown below. TREATMENT GROUP: Generate 10 sample values from a normally dis- tributed population of bone density scores with mean 0 and standard devi- ation 1. PLACEBO GROUP: Generate 15 sample values from a normally distrib- uted population of bone density scores with mean 0 and standard devia- tion 1. To generate sample data in Excel follow these steps: 1. Click the Data tab in the Ribbon. 2. Click the Data Analysis button in the Ribbon. (If Data Analysis is not available, the Analysis ToolPak must be installed as described in Section 1-40). 3. The Data Analysis dialog box now appears. 4. Select Random Number Generation, and then click OK. 5. The Random Number Generation dialog box now appears as shown. a. Select Normal in the Distribution box. b. Enter a value for the Number of Variables (or the number of col- umns of data), Number of Random Numbers, Mean, and Standard Deviation. c. Click OK to generate the values. Random Number Generation ? Number of Variables: 1 OK Number of Random Numbers: 10 Cancel Distribution: Normal Parameters Mean = 0 Standard deviation = 1 Random Seed: Output options Output Range: New Worksheet Ply: New Workbook 9.4-59 Full Alternative Text Help 9.4-59 Full Alternative Text Because each of the two samples consists of random selections from a normally distributed population with a mean of 0 and a standard deviation of 1, the data are generated so that both data sets really come from the same population, so there should be no difference between the two sample means. a. After generating the two data sets, use a 0.10 significance level to test the claim that the two samples come from populations with the same mean. b. If this experiment is repeated many times, what is the expected per- centage of trials leading to the conclusion that the two population means are different? How does this relate to a type I error? c. If your generated data leads to the conclusion that the two population means are different, would this conclusion be correct or incorrect in reality? How do you know? d. If part (a) is repeated 20 times, what is the probability that none of the hypothesis tests leads to rejection of the null hypothesis? e. Repeat part (a) 20 times. How often was the null hypothesis of equal means rejected? Is this the result you expected? Long description Random Number Generation ? Number of Variables: 1 OK Number of Random Numbers: 10 Cancel Distribution: Normal Help Parameters Mean = Standard deviation = Random Seed: Output options 0 = 1 Back Qutput Range: New Worksheet Ply: New Workbook The window displays the following entries. The number of variables, 1. The number of ran- dom numbers, 10. Distribution, normal. Parameters. Mean, 0. Standard deviation, 1. From the radio button under the heading Output options, New worksheet Ply is selected. Back