Question

10. 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 :

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.

Enter letter corresponding to most correct answer

______

Answer 1

Following table shows the calculations:

	X	(x-mean)^2
	299883	16073.82766
	299711	2044.613263
	299578	31761.44166
	299696	3626.135263
	299851	8983.741263
	299816	3573.959263
	299611	21088.09326
	299796	1582.655263
	299573	33568.61566
	299809	2786.002863
	299778	474.4816628
	299599	24717.31086
	299774	316.2208628
	299748	67.52566276
	299723	1103.395663
	299796	1582.655263
	300051	86896.78126
	299820	4068.220063
	299748	67.52566276
	299682	5508.222463
	299781	614.1772628
	299772	249.0904628
	299797	1663.220463
Total	6894393	252417.913

(i)

The sample mean is

(ii)

The sample standard deviation is

(iii)

There are 23 data values so degree of freedom is

df=n-1=23-1=22

(iv)

The critical value of t for 95% confidence interval is 2.07.

(v)

The error bound is:

(vi)

The confidence interval is