A Gallup Poll found that 51% of the people in its sample said "yes" when asked, "Would you like to lose weight?" Gallup announced: "With 95% confidence for results based on the total sample of national adults, one can say that the margin of sampling error is ± 3%."

Question

Mathematics

Rosa Cardenas

14 February, 19:28

A Gallup Poll found that 51% of the people in its sample said "yes" when asked, "Would you like to lose weight?" Gallup announced: "With 95% confidence for results based on the total sample of national adults, one can say that the margin of sampling error is ± 3%."

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Kate Schwartz · Answer 1

(a) 95% confidence interval for the percent of all adults who want to lose weight is (48%, 54%) that is between 48% and 54%

(b) to say that we have 95% confidence in this interval means that there is 95% chance that the true percentage of all adults who wants to lose weight falls in this interval.

Step-by-step explanation:

The question is missing, complete question is below:

A Gallup Poll found that 51% of the people in its sample said "yes" when asked, "Would you like to lose weight?" Gallup announced: "With 95% confidence for results based on the total sample of national adults, one can say that the margin of sampling error is ± 3%."

(a) What is the 95% confidence interval for the percent of all adults who want to lose weight?

(b) What does it mean to say that we have 95% confidence in this interval?

Confidence Interval can be calculated using p±ME where

p is the sample proportion of national adults who want to lose weight (51%) ME is the margin of sampling error (± 3%)