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

Respuesta :

Answer:

[tex]35\%[/tex] represents the sample proportion of the population

Step-by-step 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    [tex]k = 35\% = 0.35[/tex]

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

         [tex]\^ p = \frac{a+ b}{2}[/tex]

=>      [tex]\^ p = \frac{28 + 42 }{2}[/tex]

=>      [tex]\^ p = 35\%[/tex]

Hence  [tex]35\%[/tex] represents the sample proportion