Question

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?

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