Question

tp he Pew Research Center and Smithsonian magazine recently quizzed a random sample of 1006 U.S. adults on their knowledge of science. One of the questions asked, "Which gas makes up most of the Earth's atmosphere: hydrogen, nitrogen, carbon dioxide, or oxygen?" A 95% confidence interval for the proportion who would correctly answer nitrogen 0.175 to 0.225. Interpret this confidence interval.

Answer 1

Answer:

This interval (0.175, 0.225) represents the range of values that the true proportion of U.S. adults that can answer the question of 'which gas makes up the most of the atmosphere?' correctly, can take on, with a confidence level of 95%.

Step-by-step explanation:

Confidence Interval is an interval obtaimed from sample data, for the population proportion. It is an interval of range of values where the true population proportion can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample proportion) ± (Margin of error)

Margin of Error is the width of the confidence interval about the mean (sample proportion).

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the sample proportion)

Critical value is obtained from the z-tables or the t-tables depending on which information is available. For distributions where information on the population standard deviation is known or it isn't know but the sample size is large enough for the sample standard deviation can approximate the population standard deviation, the z-tables is used and for those distributions whose population standard deviation information is not known, and sample size isn't large enough, the critical value is read off the t-tables.

The critical value depends on the confidence level for both the z-tables and the t-tables critical value.

The interval obtained now represents the region of values where the true population proportion can exist within, at a certain level.of confidence.

Hope this Helps!!!