Question

Due to the popularity of instant messaging and social​ networking, informal elements such as emoticons​ (e.g., the symbol​ ":)" to represent a​ smile) and abbreviations​ (e.g., "LOL" for​ "laughing out​ loud") have worked their way into​ teenagers' school writing assignments. A survey interviewed 800 randomly selected teenagers by telephone on their writing habits.​ Overall, 431 of the teenagers admitted using at least one informal element in school writing assignments. Based on the survey​ results, construct a 90​% confidence interval for the proportion of all teenagers who have used at least one informal element in school writing assignments. Give a practical interpretation of the interval.

The 90​% confidence interval is ​( ​, ).

Interpret the interval. Choose the correct answer below.

A. One can be 10% confident that the interval contains the sample population proportion of all teenagers who have used at least one informal element in school writing assignments.

B. One can be 10% confident that the interval contains the true population proportion of all teenagers who have used at least one informal element in school writing assignments.

C. One can be 90​% confident that the interval contains the sample population proportion of all teenagers who have used at least one informal element in school writing assignments. Your answer is not correct.

D. One can be 90​% confident that the interval contains the true population proportion of all teenagers who have used at least one informal element in school writing assignments.

Answer 1

The statistical software output for this problem is:

From above output:

90% confidence interval:

(0.509, 0.568)

Interpretation:

One can be 90​% confident that the interval contains the true population proportion of all teenagers who have used at least one informal element in school writing assignments.

Option D is correct.