Question

	Country Burkina Faso Ethiopia Myanmar Ghana Kenya India Nicaragua Tunisia Guatemala Algeria Ecuador Peru Colombia Lebanon China Brazil Mexico Turkey Argentina Venezuela, RB Greece Portugal Malta Spain Italy Israel Japan France New Zealand United Arab Emirates Belgium United Kingdom Canada Germany Finland Austria Netherlands Ireland Australia Sweden United States Denmark Iceland Luxembourg Switzerland Norway	Average Income 640 660 1190 1380 1380 1680 2050 3690 3790 4270 5820 5950 6320 7680 8260 8840 9040 11180 11960 12500 18960 19850 24140 27520 31590 36190 38000 38950 39070 40480 41860 42390 43660 43660 44730 45230 46310 52560 54420 54630 56180 56730 56990 76660 81240 82330

In 2016, the global average annual income worldwide was estimated to be $10,850[1]. (This includes all countries of the world, not just the countries in the data table.)

[1] Source: Organization for Economic Co-operation and Development (OECD).

A) construct an 80%, 90%, 95%, 98%, 99% confidence interval to estimate the proportion of countries in the world with an average income greater than the global average. Calculate the Margin of Error for each confidence interval.

B) As the confidence level increases, what happens to the width of the interval? (Note: the width of the interval is the difference between the upper and lower limits.)

C) As the confidence level increases, what happens to the margin of error?

Answer 1

let x is the observation greater than 10850 = 29

using excel we have

Confidence Interval Estimate for the Proportion
Data
Sample Size	46
Number of Successes	29
Confidence Level	80%
Intermediate Calculations
Sample Proportion	0.630434783
Z Value	-1.28155157
Standard Error of the Proportion	0.07116832
Margin of error	0.091205872
Confidence Interval
Interval Lower Limit	0.539228911
Interval Upper Limit	0.721640654

Confidence Interval Estimate for the Proportion
Data
Sample Size	46
Number of Successes	29
Confidence Level	90%
Intermediate Calculations
Sample Proportion	0.630434783
Z Value	-1.64485363
Standard Error of the Proportion	0.07116832
Margin of error	0.117061469
Confidence Interval
Interval Lower Limit	0.513373314
Interval Upper Limit	0.747496251

Confidence Interval Estimate for the Proportion
Data
Sample Size	46
Number of Successes	29
Confidence Level	95%
Intermediate Calculations
Sample Proportion	0.630434783
Z Value	-1.95996398
Standard Error of the Proportion	0.07116832
Margin of error	0.139487343
Confidence Interval
Interval Lower Limit	0.490947439
Interval Upper Limit	0.769922126

Confidence Interval Estimate for the Proportion
Data
Sample Size	46
Number of Successes	29
Confidence Level	98%
Intermediate Calculations
Sample Proportion	0.630434783
Z Value	-2.32634787
Standard Error of the Proportion	0.07116832
Margin of error	0.165562269
Confidence Interval
Interval Lower Limit	0.464872513
Interval Upper Limit	0.795997052

in short we have

	margin of error	lower limit	upper limit	width
80% CI	0.0912	0.5392	0.7216	0.1824
90% CI	0.1171	0.5134	0.7475	0.2341
95% CI	0.1395	0.491	0.7699	0.2789
98%CI	0.1656	0.4649	0.796	0.3311
99%CI	0.1833	0.4471	0.8138	0.3667

2)As the confidence level increases, the margin of error is also increases
Ans 1 ) As the confidence level increases, the width of the interval is also inreases