The economic dynamism, which is the index of productive growth (in dollars) for
ID: 2946439 • Letter: T
Question
The economic dynamism, which is the index of productive growth (in dollars) for countries that are designated by the World Bank as middle-income are in following table ("SOCR data 2008," 2013):
Table: Economic Dynamism ($) of Middle Income Countries
299883
299816
299778
299796
299682
299711
299611
299599
300051
299781
299578
299796
299774
299820
299772
299696
299573
299748
299748
299797
299851
299809
299723
Compute a 95% confidence interval for the mean economic dynamism of middle-income countries by answering the following questions:
(i) Determine sample mean x :{"version":"1.1","math":"<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle mathsize="14px"><mrow><mfenced><mi mathvariant="bold">i</mi></mfenced><mo mathvariant="bold"> </mo><mo mathvariant="bold"> </mo><mi mathvariant="bold-italic">D</mi><mi mathvariant="bold-italic">e</mi><mi mathvariant="bold-italic">t</mi><mi mathvariant="bold-italic">e</mi><mi mathvariant="bold-italic">r</mi><mi mathvariant="bold-italic">m</mi><mi mathvariant="bold-italic">i</mi><mi mathvariant="bold-italic">n</mi><mi mathvariant="bold-italic">e</mi><mo mathvariant="bold"> </mo><mi mathvariant="bold-italic">s</mi><mi mathvariant="bold-italic">a</mi><mi mathvariant="bold-italic">m</mi><mi mathvariant="bold-italic">p</mi><mi mathvariant="bold-italic">l</mi><mi mathvariant="bold-italic">e</mi><mo mathvariant="bold"> </mo><mi mathvariant="bold-italic">m</mi><mi mathvariant="bold-italic">e</mi><mi mathvariant="bold-italic">a</mi><mi mathvariant="bold-italic">n</mi><mo mathvariant="bold"> </mo><menclose notation="top"><mi mathvariant="bold">x</mi></menclose><mo> </mo><mo>:</mo></mrow></mstyle></math>"}
Enter in decimal form to nearest ten-thousandth. Do not enter units of measure. Examples of correctly entered answers:
0.0015 0.0000 136.7000 99.0070 36.9128
(ii) Determine sample standard deviation s :
Enter in decimal form to nearest ten-thousandth. Examples of correctly entered answers:
0.0001 0.0020 0.5000 5.3070 1.7157
(iii) Determine degrees of freedom df value:
Enter value as whole number
(iv) Determine t score corresponding to desired confidence level
Enter value in decimal form rounded to nearest hundredth. Examples of correctly entered answers:
2.01 0.37 0.60 0.00
(v) Determine error bound of the mean:
Enter value in decimal form rounded to nearest ten-thousandth. Examples of correctly entered answers:
0.0000 0.0003 3.0060 2.0700
11.5000 27.9143 13.0000
(vi) Determine the confidence interval.
Enter lower bound value to nearest ten-thousandth, followed by < , followed by "p" for proportion or "m" for mean, followed by <, followed by upper bound value to nearest tenth. No spaces between any characters. Do not use italics. Examples of correctly entered answers:
0.7000<p<0.8010
13.1340<m<13.9113
-9.7659<m<-8.1466
(vii) Using the confidence interval, select the correct description of the result of the survey:
A. We estimate with 95% confidence that the true proportion mean economic dynamism for middle-income countries is between $40.21 and $47.54.
B. We estimate with 95% confidence that the proportional economic dynamism for middle-income countries is between $40.21 and $47.54.
C. We estimate with 95% confidence that the population amount of economic dynamism for middle-income countries is between $40.21 and $47.54.
D. We estimate with 95% confidence that the true population mean economic dynamism for middle-income countries is between $40.21 and $47.54.
299883
299816
299778
299796
299682
299711
299611
299599
300051
299781
299578
299796
299774
299820
299772
299696
299573
299748
299748
299797
299851
299809
299723
Explanation / Answer
i)
using excel
command = average(data)
mean =299756.2174
ii)
sd = stdev(data)
= 107.1146185
= 107.1146
iii)
df = n-1 = 23-1 = 22
iv)
=t.inv.2t(0.05,22)
=2.073873068
= 2.07
v)
error bound = t * s/sqrt(n) = 2.073873068* 107.1146/sqrt(23)
= 46.3198265097
= 46.3198
vi)
confidence interval =
(299756.2174 - 46.3198 , 299756.2174 +46.3198 )
= (299709.8976,299802.5372)
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