Question

justins dad claims that taking piano lessons will help justin get into an ivy league school one day. justin decides to try to prove his dad wrong by interviewing a randomly selected sample of college - educated adults. justin asks them whether they attended an ivy league school and also whether they took piano lessons as a child.
the relative frequency table below shows his results. justin interviewed 88 people who did not attend an ivy league school.

	piano lessons	no piano lessons	row total
non - ivy league	25, 91.7, 22.9	75, 91.7, 68.75	100, --, 91.7
column total	row %: --, column %: 100, total %: 25	--, 100, 75	100, 100, 100

how many adults in justins survey took piano lessons and attended an ivy league school? (round to the nearest whole number.)

does the table show evidence of an association between taking piano lessons and attending an ivy league school? choose all answers that apply:
a: yes, because 6.25% of people attended an ivy league school without taking piano lessons but only 2.1% of people took piano lessons and attended an ivy league school.
b: no, because 8.3% of people who took piano lessons attended an ivy league school, and 8.3% of all people attended an ivy league school.
c: no, because the total percentage of people who took piano lessons is less than the total percentage of people who did not take piano lessons.
d: yes, because 25% of people who attended an ivy league school took piano lessons.

Explanation:

Step1: Encontrar el porcentaje total de personas que asistieron a una escuela de la Ivy League y tomaron lecciones de piano

El porcentaje total de personas que asistieron a una escuela de la Ivy League y tomaron lecciones de piano es del 2.1% según la tabla de frecuencia relativa.

Step2: Encontrar el total de encuestados

Sabemos que 88 personas no asistieron a una escuela de la Ivy League y representan el 91.7% del total de encuestados. Sea $x$ el total de encuestados. Entonces $\frac{88}{x}=0.917$, y $x=\frac{88}{0.917}\approx96$.

Step3: Calcular el número de personas que asistieron a una escuela de la Ivy League y tomaron lecciones de piano

El 2.1% de 96 es $0.021\times96 = 2.016\approx2$.

Step4: Analizar la asociación

Para determinar si hay asociación, vemos que el porcentaje de personas que asistieron a una escuela de la Ivy League entre aquellos que tomaron lecciones de piano (8.3%) es igual al porcentaje general de personas que asistieron a una escuela de la Ivy League (8.3%). Esto significa que no hay evidencia de asociación.

Answer:

• Número de adultos que tomaron lecciones de piano y asistieron a una escuela de la Ivy League: 2
• Respuesta sobre asociación: B. No, porque el 8.3% de las personas que tomaron lecciones de piano asistieron a una escuela de la Ivy League, y el 8.3% de todas las personas asistieron a una escuela de la Ivy League.