Homework #5 - MATH 317

Confidence Intervals

 

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1. Begin by completing the values in Column B.  You should fill in each of these using equations (formulas) that depend on other cell values, not by computing the values yourself and merely typing them into the cells. 

2.  Compare the confidence interval created using the normal distribution (z-values) and the confidence interval created by using the t-distribution.  Which is wider? 

3.  Copy the contents of B3:B20 to columns C - H.  

Compare all confidence interval widths to the results computed in column B to answer the following questions. 

4.  In cell C4, change the standard deviation value from 15 to 25.  When you do this several of the values below should change.  If they did not, repeat (1) and be certain to use formulas and equations.  What happened to the width of both confidence intervals (the interval created by using the z-score and by using the t-score)?  Which is wider? 

5.  In cell D5 change the n value from 25 to 50.  Note that all other values should agree with the values in the original column B.  What happened to the width of both confidence intervals (the interval created by using the z-score and by using the t-score)?  Which is wider?  W

6.  In cell E5 change the n value from 25 to 15.  Note that all other values should agree with the values in the original column B.  What happened to the width of both confidence intervals (the interval created by using the z-score and by using the t-score)?  Which is wider? 

7.  In cell F6 change the confidence level from 0.95 to 0.80.  Note that all other values should agree with the values in the original column B.  What happened to the width of both confidence intervals (the interval created by using the z-score and by using the t-score)?  Which is wider? 

8.  For this question you will change two of the original values in Column G.  Increase the confidence level to 0.99 AND increase the standard deviation to 20.  Note that all other values should agree with the values in the original column B.  What happened to the width of both confidence intervals (the interval created by using the z-score and by using the t-score)?  Does this seem reasonable from earlier changes you have made?  Give specific references here to previous questions or columns.

9.  For this question you will change two of the original values in Column H.  Increase the confidence level to 0.99 AND increase the number of subjects to 50.  Note that all other values should agree with the values in the original column B.  What happened to the width of both confidence intervals (the interval created by using the z-score and by using the t-score)?  Does this seem reasonable from earlier changes you have made?  Give specific references here to previous questions or columns.

Print out Cells A1:H23.

Report Confidence Level, Alpha, t value, and z value to 2 decimal places. 

Report SE, Confidence Interval Range, Lower Limit & Upper Limit to 1 decimal place.

Report df as a whole number.

10.  Finally, finish the following sentences AND cite a previous question as evidence:

(a)  All other values being equal, if you decrease the standard deviation, you will ________ the confidence interval width.  Question # _______

(b)  All other values being equal, if you decrease the sample size, you will ______ the confidence interval width.  Question # _______

(c)  All other values being equal, if you decrease the confidence level, you will ______ the confidence interval width.  Question # _______

(d)  All other values being equal and a small sample size, the t-distribution will create a confidence interval that is _________ than the confidence interval created by the z-distribution (normal distribution).  Question # _________