Question

Environmental engineers are using data collected by weather data centers to learn how climate affects the sea ice. Of 506 ice melt ponds studied in a certain​ region, 94 were classified as having​ "first-year ice". The researchers estimated that about 19​% of melt ponds in the region have​ first-year ice.​ Estimate, with​ 90% confidence, the percentage of all​ ice-melt ponds in the region that have​ first-year ice. Give a practical interpretation of the results.

Answer 1

Solution :

Given that,

n = 506

x = 94

= x / n = 94 / 506 = 0.186

1 - = 1 - 0.186 = 0.814

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.96 * (((0.186 * 0.814) / 506)

= 0.029

A 95% confidence interval for population proportion p is ,

- E < P < + E

0.186 - 0.029 < p < 0.186 + 0.029

0.157 < p < 0.215

A 95% confidence interval for population proportion p is : (0.157 , 0.215)