These problems must be solved using an Excel spreadsheet and formulas. Make sure

Question

These problems must be solved using an Excel spreadsheet and formulas. Make sure your work is displayed in a clear manner. Reference the attached spreadsheet file for the data “Ch08 Quiz 3.xlsx”and use it to complete the work for these problems. Submit your work as directed.

1. Data are shown for a random sample of weights in the attached spreadsheet (problem 1 sheet). The population has a known standard deviation () of 51 pounds. Compute a 95% confidence interval for the mean of the population.

2. Data are shown for a random sample of times to close a home purchase in the attached spreadsheet (problem 2 sheet). Provide a 95% confidence interval for the closing time.

3. Consider the weight data from problem 1. This data is included again on the problem 3 sheet of the referenced spreadsheet. The population standard deviation for weights is estimated to be 51 pounds. How large of a sample must be taken in order to be 93% confident that the margin of error will not exceed 5 pounds?

EXCEL SPREADSHEET INFO

Explanation / Answer

1.

Note that              
              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    155.4166667          
t(alpha/2) = critical t for the confidence interval =    2.20098516          
s = sample standard deviation =    51          
n = sample size =    12          
df = n - 1 =    11          
Thus,              
              
Lower bound =    123.0128126          
Upper bound =    187.8205207          
              
Thus, the confidence interval is              
              
(   123.0128126   ,   187.8205207   ) [ANSWER]

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If you use z distribution, please consider this ALTERNATIVE:

Note that              
              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    155.4166667          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
s = sample standard deviation =    51          
n = sample size =    12          
              
Thus,              
              
Lower bound =    126.5612304          
Upper bound =    184.2721029          
              
Thus, the confidence interval is              
              
(   126.5612304   ,   184.2721029   ) [ALTERNATIVE ANSWER USING Z]

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Hi! Please submit the next part as a separate question. Please include the data for part 2 and 3 as well. That way we can continue helping you! Please indicate which parts are not yet solved when you submit. Thanks!

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