A streaming service company plans to introduce a new premium tier and wants to estimate the worldwide percentage of its users who intend to subscribe. Based on a pilot, $20\%$ of users indicated they plan to upgrade. The marketing team needs a $90\%$ confidence interval with a margin of error of $3$ percentage points. How many users must be surveyed? Can the team simply poll their own friends and colleagues instead of drawing a random sample? Explain.

$658$

Yes, because with $n=482$, the central limit theorem applies, and any sample (even friends) will give an approximately valid margin of error.

$482$

No. Polling friends is a convenience sample that introduces selection bias and breaks the random sampling assumption, so the $90\%$ CI would not be valid.

$598$

Yes, if they can post‐stratify (weight) the friends’ responses to match known user demographics, correcting for the bias.

$344$

No. Unless they can show that their friends’ upgrade intentions are exchangeable with the global population, the sample will be a valid generalization.