Question

The culinary herb cilantro, Coriandrum sativum, is very polarizing; some people love it and others hate it. A genetic component is suspected to be at play. A survey of 12087 American adults of European ancestry asked whether they like or dislike the taste of cilantro. A total of 3181 said that they dislike the taste of cilantro.

STATE: Estimate with 95% confidence the proportion of all American adults of European ancestry who dislike the taste of cilantro.

PLAN: We will give a 95% confidence interval for p.

SOLVE: We have an SRS with sufficiently large sample size, so we can use the large‑sample method. Calculate p^ for the large‑sample method. (Enter your answer rounded to four decimal places.)

p=

SEp=

Calculate the bounds of the 95% confidence interval

lower=

uppper=

Answer 1

Solution :

n = 12087

x = 3181

= x / n = 3181 / 12087 = 0.2632

1 - = 1 - 0.2632= 0.7368

At 95% confidence level the z is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.960

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.960 * (((0.2632 * 0.7368 ) / 12087)

= 0.0078

A 95 % confidence interval for population proportion p is ,

- E < P < + E

0.2632 - 0.0078 < p < 0.2632 + 0.0078

0.2553 < p < 0.2710