In the given question your total number of books age year 11 so I am taking n=11. To construct a confidence interval estimate of the mean age of all books in the library based on the sample provided, we first need to determine the sampling procedure used to collect these ages. Since you mentioned that you grabbed 10 books randomly, it seems like a simple random sampling method was employed.

Simple random sampling involves randomly selecting items from the entire population without any specific pattern or bias. In this case, you randomly selected 10 books from the library, and the years of publication of these books are:

1999,1995,2011,2011,2007,2013,1999,2016,2001,2008,2009

Now, to construct a confidence interval estimate of the mean age of all books in the library, we'll calculate the sample meanx and the sample standard deviation s from the given ages. Then, we'll use these values along with the desired confidence level to determine the confidence interval.

1. Calculate Sample Mean x:

x=ni=1nxi

Wherexi represents each individual age and n is the sample size.

x=111999+1995+2011+2011+2007+2013+1999+2016+2001+2008+2009x=1122069=2006.273

2. Calculate Sample Standard Deviation s:

s=n1i=1n(xix)2s=111(19992006.273)2+(19952006.273)2+...+(20092006.273)2s=10456.182s45.6182s6.754

3. Choose Confidence Level and Find Critical Value:

Let's assume a 95% confidence level for this estimation. The critical value for a 95% confidence level with a sample size of 11 can be found using a t-distribution table or statistical software. For a 95% confidence level and 10 degrees of freedom, the critical value is approximately 2.228.

4. Calculate Margin of Error E:

E=ntsE=112.2286.754E1115.049E3.316615.049E4.54

5. Construct Confidence Interval:

ConfidenceInterval=(xE,x+E)ConfidenceInterval=(2006.274.54,2006.27+4.54)ConfidenceInterval=(2001.73,2010.81)

Therefore, with 95% confidence, we estimate that the mean age of all books in the library is between 2001.73 and 2010.81 years.

Use the mean and the standard deviation obtained from the last question and test the claim that the mean age of all books in the library is greater than 2005.