Question

Economist David Galenson has studied types of creativity, both early achievers who create masterpieces at an...

Economist David Galenson has studied types of creativity, both early achievers who create masterpieces at an early age and late bloomers whose great work comes later in life. In one of his studies, he determined which American poems are featured in the most anthologies (and therefore considered the best), and he recorded the ages at which the poet wrote each poem. The data is presented below:

Poet

Poem

Age

Eliot

Prufrock

23

Lowell

Skunk Hour

41

Frost

Stopping by the Woods on a Snowing Evening

48

Williams

Red Wheelbarrow

40

Bishop

The Fish

29

Pound

The River Merchant’s Wife

30

Plath

Daddy

30

Frost

Mending Wall

38

Stevens

The Snow Man

42

Williams

The Dance

59

  1. Find a confidence interval for the population proportion of all poets who were at least 40 when they wrote their best poem. Use a confidence level of 99%. Use proper notation and circle your final answer. (Round to four decimal places.)

  2. (f) Fill in the blanks given in the statement below to interpret your interval.
    “I am confident that the proportion of poets who were at least 40 when they wrote their best poem is between and .”

  3. (g) How many poets would David Galeson need to survey in order to produce a 90% confi- dence interval with a margin of error of .03?

Homework Answers

Answer #1

(e) The 99% confidence interval for the population proportion of all poets who were at least 40 when they wrote their best poem is between 0.0927 and 0.9073.

Observed
0.5 p (as decimal)
5/10 p (as fraction)
5. X
10 n
0.1549 std. error
0.0927 confidence interval 99.% lower
0.9073 confidence interval 99.% upper
0.4073 margin of error

(f) I am confident that the proportion of poets who were at least 40 when they wrote their best poem is between 0.0927 and 0.9073.

(g) n = (1.645/0.03)^2*0.5*0.5 = 752

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