Question

After all necessary conditions were checked in a study involving 210 randomly-selected American adults, a 950 confidence interval for the proportion of all American adults that drink coffee regularly was correctly computed to be (0.34,0.48). Use this information to answer (a) - (d). Unsupported answers will not receive credit. [1 pt) (a) What is the statistic that was used to construct this confidence interval? Include both the statistic's symbol and value in your sentence answer. [1 pt] (b). How many American adults in the 210-person sample drink coffee regularly? [1 pt] (c) What is the margin of error in the 95% confidence interval (0.34,0.48) ? [1 pt] (d) In the context of this problem, does the 95% confidence interval (0.34,0.48) mean there's a 95% chance that the percentage of American adults that drink coffee regularly is between 34% and 48% ? In other words, is P(0.34<

p^ <0.48)≐0.95 a true statement? Why or why not? Explain clearly and completely.

Answer 1

The statistic used to construct the confidence interval is the proportion of American adults that drink coffee regularly. The 95% confidence interval does not mean there's a 95% chance that the percentage of American adults that drink coffee regularly is between 34% and 48%.

Step-by-step explanation:

(a) The statistic used to construct this confidence interval is the proportion of American adults that drink coffee regularly. The symbol for this statistic is p-hat, and in this case, the value is between 0.34 and 0.48.

(b) To find the number of American adults in the 210-person sample who drink coffee regularly, we multiply the proportion by the sample size. So, the number of American adults who drink coffee regularly is between 0.34 * 210 = 71.4 and 0.48 * 210 = 100.8.

(c) The margin of error in the 95% confidence interval can be found by subtracting the lower bound from the upper bound. So, the margin of error is 0.48 - 0.34 = 0.14.

(d) The 95% confidence interval does not mean there's a 95% chance that the percentage of American adults that drink coffee regularly is between 34% and 48%. Instead, it means that if we were to repeat the study multiple times, 95% of the confidence intervals constructed using the same method would contain the true proportion of American adults who drink coffee regularly.