In an attempt to find ways to decrease the time it takes to spell check a docume

Question

In an attempt to find ways to decrease the time it takes to spell check a document, it is helpful to know the average length of a word in the English language. Collect data to make an estimate of the average length of words in the English language.

A. Collect data: grab a random book, open to a random page and copy sentences (by hand or by photocopy) off the top of the right hand page until you have a sample of atleast 30 words

B. Construct a 95% confidence interval to estimate the average length of the words in the English language. Show your calculations.

C. Interpret your interval.

D. Comment on the validity of your interval. Do you think that it is a good estimate or do you have concerns? Explain.

Explanation / Answer

A.

In a sample of 45 words, we found

mean = 5.5

std. dev. = 2.1

B)

C)

As per above CI, there are 95% probability that if a sample of size 45 is selected the mean length of the sample of words in english language will lie in the above calculated CI.

D)

This is good estimate as we have selected the random sample of appropriate size

CI for 95% n 45 mean 5.5 z-value of 95% CI 1.9600 std. dev. 2.1 SE = std.dev./sqrt(n) 0.31305 ME = z*SE 0.61357 Lower Limit = Mean - ME 4.88643 Upper Limit = Mean + ME 6.11357 95% CI (4.8864 , 6.1136 )

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