Go to a local library; collect a sample of books consisting of the ages of book (based on copyright dates). Plan and describe the sampling procedure, then use the results to construct a confidence interval estimate of the mean age of all books in the library. Please, post and share your results with the class.
Based on copyright dates, my sample of books consisted of ages 1992, 1999, 2004, 2013, 2002 and 2014.
The sample mean is: 2004
The sample standard deviation: is 8.4
n=6
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability (for 95%, use .025) and its Z score.
95% = mean ± Z SEm
SEm = SD/√n
For other intervals, adjust Z score accordingly.
How would you solve this with the same information. Please I need help Im clueless!!
Use the mean and the standard deviation obtained from the last module and test the claim that the mean age of all books in the library is greater than 2005. Share your results with the class
Oh, I'm sorry! I don't have the ability to physically go to a library and collect sample data. But don't worry, I'm here to provide a different kind of help!
To construct a confidence interval estimate of the mean age of all books in the library, we can follow the steps below:
Step 1: Determine the confidence level. Let's assume a confidence level of 95%. This means that we want to be 95% confident that our interval contains the true mean age of all the books in the library.
Step 2: Calculate the margin of error. The margin of error is determined by the confidence level and the sample standard deviation. For a 95% confidence level, we can use the t-distribution with (n-1) degrees of freedom to calculate the margin of error. The formula for the margin of error is given by:
Margin of Error = t (standard error)
where t is the t-value corresponding to the desired confidence level and the standard error is calculated as:
Standard Error = sample standard deviation / sqrt(n)
Using the given sample standard deviation of 8.4 and sample size of 6, the standard error is:
Standard Error = 8.4 / sqrt(6) = 3.43
To find the t-value, we need to determine the degrees of freedom. Since our sample size is 6, the degrees of freedom is (6-1) = 5. Consulting the t-distribution table for a 95% confidence level and 5 degrees of freedom, we find the t-value to be approximately 2.571.
Therefore, the margin of error is:
Margin of Error = 2.571 * 3.43 = 8.84
Step 3: Calculate the confidence interval. The confidence interval is calculated by subtracting and adding the margin of error to the sample mean.
Confidence Interval = sample mean +/- margin of error
Using the sample mean of 2004 and the margin of error of 8.84, we can calculate the confidence interval as:
Confidence Interval = 2004 +/- 8.84
Confidence Interval = (1995.16, 2012.84)
Therefore, with 95% confidence, we estimate that the mean age of all books in the library is between 1995.16 and 2012.84.
To construct a confidence interval estimate of the mean age of all books in the library, we first need to determine the desired level of confidence. Let's assume a 95% confidence level, which is commonly used.
To calculate the confidence interval, we will use the formula:
Confidence Interval = Sample Mean ± (Critical Value * Standard Error)
Here are the steps to calculate the confidence interval:
Step 1: Calculate the standard error. The standard error measures the average variability of the sample mean from the true population mean. It can be calculated using the formula:
Standard Error = Sample Standard Deviation / sqrt(sample size)
For our sample, the standard error would be:
Standard Error = 8.4 / sqrt(6)
Step 2: Determine the critical value. The critical value is based on the desired level of confidence and the sample size. To find the critical value, we need to refer to the t-distribution table since the sample size is small.
For a 95% confidence level and a sample size of 6, the critical value is approximately 2.571.
Step 3: Calculate the confidence interval. Plug the values from step 1 and step 2 into the formula mentioned earlier.
Confidence Interval = Sample Mean ± (Critical Value * Standard Error)
Confidence Interval = 2004 ± (2.571 * (8.4 / sqrt(6)))
Now, let's do the calculation:
Confidence Interval = 2004 ± (2.571 * (8.4 / sqrt(6)))
Confidence Interval = 2004 ± (2.571 * 3.43)
Calculating this, we get:
Confidence Interval = 2004 ± 8.83
Therefore, the confidence interval estimate of the mean age of all books in the library is (1995.17, 2012.83) at a 95% confidence level.
Please note that the confidence interval estimate assumes that the sample is representative of the entire population of books in the library, and that the sampled books were selected randomly.