Question

A TV report conducted a survey of 947 people in New York City and found that 35% of the population believe that the Yankees will miss the playoffs this year. In the accompanying dialogue, the reporter states, we are 97% confident that the true proportion of people in New York City who believe that the Yankees will miss the playoffs this year lies between 28% and 42% . What does 35% represent in the report

Answer 1

`35\%` represents the sample proportion of the population

Explanation:

From the question we are told that

The sample size is n = 947

The proportion of the population that believes that the Yankees will miss the playoffs this year is
`k = 35\% = 0.35`

From the question we are told the confidence level is 97%

The lower limit of the confidence level is a = 28%

The upper limit of the b = 42%

Generally the sample proportion of this population is mathematically represented as

`\^ p = (a+ b)/(2)`

=>
`\^ p = (28 + 42 )/(2)`

=>
`\^ p = 35\%`

Hence
`35\%` represents the sample proportion