Testing a Claim

This is the question that needs to be answered:

Use the mean and the standard deviation obtained from the last module (see below) and test the claim that the mean age of all books in the library is greater that 2005. Share your results with the class. 

This is my answer to the discussion from the last module:

I collected a sample of books consisting of the ages (based on copyright dates). The science section of the library had about 400 books arranged on shelves in the order of their library codes and alphabetical order of writers. Most of the books in the lab were published in the 1990s.

Sampling Method

I used deck cards, apart from the face and joker cards, including only non paints (2 to 10) and aces (1). The cards were shuffled sufficiently to ensure the card selected was random. Beginning with the first set of cards, I would turn a card to reveal its number (N) then I would proceed to the Nth book on the shelf. I repeated the same procedure until I picked 21 books (the anticipated number being   = 19.6 20 books. 

The samples collected were presented in the order of the date

1967, 1968, 1969, 1975, 1979, 1983, 1984, 1984, 1985, 1989, 1990, 1990, 1991, 1991, 1991, 1991, 1992, 1992, 1992, 1997, 1999

Confidence Interval Estimate

Mean date =  =1985.67

Variance = 84.93 (sum of (year-mean) 2  

Sample Standard Deviation = Övariance = 9.2

Using the empirical rule,

68 percent of the data values are within one S.D of the mean.

95 percent of the data are within two S.D of the mean.

99.73 percent of the data are within three S.D of the mean.

Lower limit = mean + sample’s S.D = 1985.67 + 9.2 = 1994.87

Upper limit = mean – sample’s S.D = 1985.67 - 9.2 = 1976.47

In short 68% of the books in that section of the library were published between 1994.87 and 1976.47

For 95% data:

Lower limit = mean – 2 × sample’s S.D = 1967.27

Upper limit = mean + 2 × sample’s S.D = 2004.07

Therefore 95% of the books were between 1967.27 and 2004.07.

For 99.73% data 

Lower limit = mean – 3 × sample’s S.D = 1958.07

Upper limit = mean + 3 × sample’s S.D = 2013.27

Therefore 99.73% of the books were between 1958.07 and 2013.27.