Question

Recall that you took samples of words from the population of words in the Gettysburg Address, for which the average length of a word is 4.295 letters.
1.Is the number 4.295 a parameter or a statistic?
2.When you first selected your sample of 10 (circled) words, what was the variable that you recorded about the words? Was the variable categorical or quantitative?
3.You calculated the average (mean) number of letters per word in your sample of ten circled words. Is this value a parameter or a statistic?
4.Students in our class produced a graph on the board that displayed the sample mean word lengths. What aspect of the graph indicated that the sampling method was biased?
5.Would selecting words by closing your eyes and pointing at the page 10 times produce an unbiased sampling method? Explain briefly.

Answer 1

1.

4.295 is a statistic.

(statistic is a function of sample values taken from population, here 4.295 is value of sample mean which is the function(here average) of the length of sample words

2.

Quatntitative

(since we are interested in finding average length of words, we need to count the letters present in each word. Hence the number of letters in a word is a variable which can take value as 1,2,3 an so on.)

3.

The value is statistic.

(the mean number of letters per word is calculated by taking average of number of letters in each of 10 words sampled.

And statistic is the function of sample values of variable from population.)

4.

As the mean length of words is looks so small,

While plotting the graph, it may have been seen that the length of every of 10 words is small liying around 4 or 5, or a pattern in which students has selected words like increasing letters or decreasing letters by going on selecting words or the student might have selected the words he/she likes.

Hence this indicates Bias as the length of word should be randomly spread for 10 words , and the students has circled by his/her choice.

5.

Yes. This procedure will be unbiased sampling method as student won't be able to select the words by his/her choice. By randomly pointing out at the page, we would get the lengths of word at random without any pattern. And we will get a good randomly spread data(length of words)