Question

2020 Election ~ Bernie Sanders is a popular presidential candidate among university students for the 2020 presidential election. Leading into Michigan’s presidential primary election in 2020, a journalist, Lauren, took a random sample of 12133 university students and found that 9674 of them support Bernie Sanders. Using this data, Lauren wants to estimate the actual proportion of university students who support Bernie Sanders.

We want to use statistical inference to estimate the actual proportion of university students who support Bernie Sanders.

To use a normal distribution in this scenario, which of the following conditions must be satisfied?

	The observations within the sample must be independent of each other.
	Both n×p0n×p0 and n×(1−p0)n×(1-p0) must be at least 10 where p0p0 is the null value for the population proportion.
	There must be at least 10 observed successes and 10 observed failures in the sample.
	Any two samples must be independent of each other.

Answer 1

To find the confidence interval or actual proportion

We first need to check

If n*p and n*(1-p) both are greater than 10

Or at least 10

To satisfy the conditions of normality

So answer is

There must be at least 10 observed successes and 10 observed failures in the sample.