Question

Environmental engineers are using data collected by weather data centers to learn how climate affects the sea ice. Of 515 ice melt ponds studied in a certain​ region, 78 were classified as having​ "first-year ice". The researchers estimated that about 15​% 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.

Construct a 90% confidence interval around the sample proportion of ice melt ponds with the first-year ice.

Answer 1

Given : n=515 , X=78

The estimate of the sample proportion is ,

Now , the critical value is , ; From Z-table

Therefore , the 90% confidence interval around the sample proportion of ice melt ponds with the first-year ice is ,

Now , the null and alternative hypothesis is ,

Here , the value 0.15 lies in the confidence interval.

Therefore , fail to reject Ho.

Conclusion : The researchers estimated that about 15​% of melt ponds in the region have​ first-year ice